Connecticut Common Core Algebra 1 Curriculum. Professional Development Materials. Unit 4 Linear Functions

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1 Connecticut Common Core Algebra Curriculum Professional Development Materials Unit 4 Linear Functions Contents Activit 4.. What Makes a Function Linear? Activit 4.3. What is Slope? Activit 4.3. Horizontal and Vertical Lines Activit 4.4. Effects of Changing Parameters Activit 4.6. Trends in Bottled Water Consumption Activit 4.6. Point-Slope Form of an Equation Activit Finding and Using Linear Equations Eit Slip 4.. Distance and Time* Eit Slip 4.. Motion Detector* Eit Slip 4.3. Population Growth* Eit Slip 4.4. M Linear Function* Unit 4 Performance Task: State of the States* Unit 4 Mid-Unit Test* Unit 4 End-of-Unit Test* * These items appear onl on the password-protected web site.

2 Name: Date: Page of What Makes a Function Linear? Linear functions have graphs that are straight lines while nonlinear functions have graphs that are NOT straight lines. If a graph is made up of two or more pieces of lines, then that graph is a special tpe of linear function called a piecewise linear function.. Determine which graphs are linear and which graphs are nonlinear. A B C D Distance-time functions describe the distance between a person and an object over time. A distance-time function ma be linear or non-linear, increasing, decreasing, or constant, depending on the tpe of movement. To describe a distance-time function, tell (a)where the object starts, (b)what direction it moves, (c)how fast it moves and (d)whether it is speeding up, slowing down or moving at a stead rate.. Suppose a person s distance from a motion detector is changing over time. a. Identif the independent variable in this situation. b. Identif the dependent variable in this situation. Activit 4.. CT Algebra I Model Curriculum Version 3.0

3 Name: Date: Page of We will now create graphs of distance-time functions to match descriptions of movements. The graphs should show a person s distance from a motion detector sensor over time. 3. Sketch the distance-time graphs for the following scenarios. a. Stand one meter from the sensor, walk at a constant (stead) slow pace awa from the sensor. b. Stand one meter from the sensor, walk awa from the sensor changing our pace from slow to fast. d t c. Stand one meter from the sensor, and as ou walk awa, change our pace from fast to slow. d d t d. Stand five meters from the sensor and walk toward the sensor at a constant rate. d t t Activit 4.. CT Algebra I Model Curriculum Version 3.0

4 Name: Date: Page 3 of e. Stand five meters from the sensor and walk towards the sensor slowl at first, then speed up. f. Stand five meters from the sensor and walk toward the sensor quickl at first, then slow down. d g. Stand one meter from the sensor and stand still the whole time. t d d h. Stand one meter from the sensor and stand still for 3 seconds, then walk awa at a constant rate. t d t t 4. a. Describe an similarities among the graphs in 3a, 3b and 3c. b. What are differences between the graph 3a and the graphs 3b and 3c?. Which of the graphs in question (3) could be considered linear and which are nonlinear? Linear: Nonlinear: Activit 4.. CT Algebra I Model Curriculum Version 3.0

5 Name: Date: Page 4 of 6. Describe a scenario of someone walking/running that could create the graphs below. A B 7 Distance Distance Time Time A: B: 7. Describe a motion that creates a linear function. 8. Describe a motion that creates a non-linear function. Activit 4.. CT Algebra I Model Curriculum Version 3.0

6 Name: Date: Page of 9. The following table has values collected from measuring a person who attempted to walk at a constant rate. Use the data to determine whether or not the person was successful. Support our answer with a graph. Time Distance (# of seconds) (# of feet) Distance (feet) Time (seconds) Activit 4.. CT Algebra I Model Curriculum Version 3.0

7 Name: Date: Page of 7 What is Slope? What is slope? If ou have ever walked up or down a hill, then ou have alread eperienced a real life eample of slope. Keeping this fact in mind, b definition, the slope is the measure of the steepness of a line. In math, slope is defined from left to right. There are four tpes of slope ou can encounter. A slope can be positive, negative, zero, or undefined. Positive slope: Negative slope: Zero slope: Undefined slope: If ou go from left to right and ou go up, the line has a positive slope. If ou go from left to right and ou go down, the line has a negative slope. If ou go from left to right and ou don t go up or down, the line has a zero slope. If ou can onl go up or ou can onl go down, the line has an undefined slope. Here is one method of finding the slope of a line. Remember, slope is a measure of how steep a line is. That steepness can be measured with the following formula. rise slope = run Let s illustrate with two eamples: For this situation, we see that the rise is and the run is 4. So, the slope = or after simplification. Since is positive, 4 ou are going uphill. Ever time ou go up unit, ou go across or horizontall to the right units. For this situation, we see that the rise is - and the run is 3. So, the slope =. Since is negative, ou are going downhill. 3 3 Ever time ou go down units, ou go horizontall to the right 3 units. Activit 4.3. CT Algebra I Model Curriculum Version 3.0

8 Name: Date: Page of 7. Find the rise and the run for each solid line. Then state the slope of the solid line. Remember, slope is defined from left to right. a. b. Rise = Run = Slope = Rise = Run = Slope =. Starting at point A find the rise and run to get to point B. Then connect the points to make a solid line. Identif the rise, run, and slope for the line segment between each pair of points below. a. b. B A - - A B - - Rise = Rise = Run = Run = Slope = Slope = Activit 4.3. CT Algebra I Model Curriculum Version 3.0

9 Name: Date: Page 3 of 7 3. Use the coordinate plane below B C 8 A -4-6 a. Connect the points using a straightedge. Etend the line past points A and C and place arrows at each end. b. Find the slope between points A and B. Rise = Run = Slope = c. Find the slope between points B and C. Rise = Run = Slope = d. Find the slope between points A and C. Rise = Run = Slope = e. What can ou conclude about the slope of this line looking at our results in parts b thru d? f. Starting at point C find a fourth point which would belong to the same line. Label our fourth point D and eplain how ou arrived at it using what ou know about slope. Activit 4.3. CT Algebra I Model Curriculum Version 3.0

10 Name: Date: Page 4 of 7 4. Now, let s see how to find the slope when we don t know the rise and the run. If we graph the slope on the coordinate sstem, we will be able to derive another formula for slope using the and values of the coordinates. a. Let s put a line with a slope of on the coordinate sstem. 3 Begin b plotting the point (, 3) and labeling it point A. From point A do the rise and run for the slope that is /. Plot this second point, and label it point B. Connect the points using a straight edge and name the coordinates of point A and point B. Etend the line past points A and B and place arrows at each end. 4 b. Write the ordered pair for the points: A (, ) B (, ) c. The two coordinates for points A and B can be used to get the slope of Let us find the difference in the -coordinates:. Since we cannot call both coordinates, we can call one and call the other. Let represent the -coordinate of point A. Therefore, = Let represent the -coordinate of point B. Therefore, = Now subtract = The difference in the -coordinates can be epressed as. This is the RISE. Let us find the difference in the -coordinates: Since we cannot call both coordinates, we can call one and call the other. Let represent the -coordinate of point A. Therefore, = Let represent the -coordinate of point B. Therefore, = Now subtract = The difference in the -coordinates can be epressed as. This is the RUN. Activit 4.3. CT Algebra I Model Curriculum Version 3.0

11 Name: Date: Page of 7 The formula for the slope between the two points A and B can be found b using the and coordinates of the two points. Call the ordered pair for point A (, ) and the ordered pair for point B (, ).. Use the formula above to find the slope of the line passing through the given points. Show our work. a. (, ) & (, 9) b. (, 4) & (, ) = = = = = = = = c. (4, 0) & (8, -) d. (-8, 6) & (3, 4) = = = = = = = = Activit 4.3. CT Algebra I Model Curriculum Version 3.0

12 Name: Date: Page 6 of 7 e. (-3, -) & (-, -) f. (0, 7) & (, 0) = = = = = = = = Slope is a measure of steepness and direction. Slope describes a rate of change. 6. Todd had gallons of gasoline in his motorbike. After driving 00 miles, he had 3 gallons of gasoline left. The graph below shows Todd s situation. Gas in Tank (in gallons) Miles Driven 0 a. What are the coordinates of two points that ou could use to find the slope of the line? A (, ), B (, ) b. What is the slope of the line? Write in fraction form and use the units of measure ou find on the and aes. c. Write the slope as a unit rate that will be in gallons per mile. Activit 4.3. CT Algebra I Model Curriculum Version 3.0

13 Name: Date: Page 7 of 7 A rate is a ratio that compares two units of measure. An eample of a rate in fraction form is. Slopes are rates. You can rename rates like ou rename fractions. In this eample divide the numerator and denominator b 0, to obtain an equivalent rate of. Divide the numerator and denominator b to obtain in the denominator.. This is a unit rate, because is Writing the fraction in decimal form gives hour is the rate of pa. This is also a unit rate.. In ever da language, we sa $8.0 per One wa to obtain a unit rate is to rewrite the fraction so the denominator is. You can also think of renaming the fraction to decimal form. 7. Sam and Kim went on a hike. The graph at the right shows their situation. a. Find the slope of Kim s hike. (Alwas include units of measure.) b. Write Kim s slope as a unit rate. Distance (in miles) 4 KIM Time (in hours) SAM 3 c. Find the slope of Sam s hike. d. Write Sam s slope as a unit rate. e. Who is hiking at a faster speed, Kim or Sam? Eplain how ou know b looking at the graph and b using the numbers for slope that ou obtained above. Activit 4.3. CT Algebra I Model Curriculum Version 3.0

14 Name: Date: Page of 4 Horizontal and Vertical Lines Warm Up: Simplif: a = b = c. 3 3 = 6 6 State a conclusion: If zero is in the numerator of a fraction, but not in the denominator, the fraction equals. If zero is in the denominator of a fraction, the fraction is. Tell whether or not the graphs below displa a function. Calculate the slope (m) of each line. You ma either find the rise and run directl from the graphs or use the slope formula to get our answers. Write our answers as a fraction and then simplif the fraction if possible. Hint: Pick eas points from each line to work with. A B Function: es or no? Function: es or no? Slope of Line A Slope of Line B State a conclusion: The slope of a horizontal line equals. Activit 4.3. CT Algebra I Model Curriculum Version 3.0

15 Name: Date: Page of 4. Complete a table for each function below and then plot the points from the table on the following coordinate plane. Using a ruler, connect the points on each coordinate plane. a. = is the same as b. = 4 is the same as State a conclusion: An equation of the form = will be a horizontal line. 3. Which of the following equations will give a graph that is a horizontal line? (Circle all that appl.) a. = + b. = 7 c. = 3 d. = 0 + e. = 0 f. = 4. The slope formula is:. Find the slope between the two points using the slope formula. a. (,-3) and (-,-3) b. (-4,4) and (,4) Activit 4.3. CT Algebra I Model Curriculum Version 3.0

16 Name: Date: Page 3 of 4 6. Without using the slope formula, how can ou tell if the slope of a line between two points will be zero just b looking at the two points? 7. Tell whether or not the graph displas a function. Calculate the slope (m) of each line. You ma either find the rise and run directl from the graph or use the slope formula to get our answers. Write our answer as a fraction and then put the fraction in simplest form. Hint: Pick eas points from each line to work with. A B Function: es or no? Function: es or no? Slope of Line A Slope of Line B State a conclusion: The slope of a vertical line is. Activit 4.3. CT Algebra I Model Curriculum Version 3.0

17 Name: Date: Page 4 of 4 8. Complete a table for each equation below and plot the points from the table on the following coordinate plane. Using a ruler, connect the points on each coordinate plane. a. = is the same as b. = 4 is the same as State a conclusion: An equation of the form = will be a vertical line. 9. Which of the following equations will give a graph that is a vertical line? (Circle all that appl.) a. = 0 b. = 7 c. = d. = e. = 0 f. + = 0 0. Find the slope between the two points using the slope formula. a. (,3) and (,) b. ( 4,4) and ( 4,7). Without using the slope formula, how can ou tell if the slope of a line between two points will be undefined just b looking at the two points? Activit 4.3. CT Algebra I Model Curriculum Version 3.0

18 Name: Date: Page of 6 Effects of Changing Parameters In this activit, ou will learn how the parameters (numbers) m and b affect a linear function in the form = m+ b. The form = m + b is known as slope-intercept form. Instructions: We will use our graphing calculators to eplore linear functions. First, we need a good window. The window controls the range of and values displaed on the graphing calculator. We will use a window where the -ais will go from negative five to five, and the -ais will go from negative five to five. To do this: a. Turn the calculator ON. b. Press the WINDOW button. c. In the WINDOW menu, set Xmin = -, Xma =, Xscl =, Ymin = -, Yma =, Yscl = d. Enter the function: = + 0 into the graphing calculator. To do this: Press the Y= button. Enter our equation into Y=. For the -variable, the button is the X,T,Θ,n button. e. Graph the function. To do this, press the GRAPH button.. Sketch the graph of! =! + 0. a. What is the slope? b. What is the value of b in the equation? - c. What is the -intercept? Activit 4.4. CT Algebra I Model Curriculum Version 3.0

19 Name: Date: Page of 6. Graph! =! + 0 in the calculator and sketch the graph. a. What changed from the graph in question ()? b. What is the slope? c. What is the value of b in the equation? - d. What is the -intercept? 3. Graph! =!! + 0 in the calculator and sketch the graph.! a. What changed from the graph in question ()? b. What is the slope? c. What is the value of b in the equation? d. What is the -intercept? Activit 4.4. CT Algebra I Model Curriculum Version 3.0

20 Name: Date: Page 3 of 6 4. If m is a positive number, what happens to the graph of a linear function as m increases?. If m is a positive number, what happens to the graph of a linear function when m decreases but remains positive? 6. Graph! =! + 0 in the calculator and sketch the graph. a. What changed from the graph in question ()? b. What is the slope? c. What is the value of b in the equation? d. What is the -intercept? 7. Graph! =! + 0 in the calculator and sketch the graph. a. What changed from the graph in question (6)? b. What is the slope? c. What is the value of b in the equation? d. What is the -intercept? Activit 4.4. CT Algebra I Model Curriculum Version 3.0

21 Name: Date: Page 4 of 6 8. Graph! =!! + 0 in the calculator and sketch the graph.! a. What changed from the graph in question (6)? b. What is the slope? - - c. What is the value of b in the equation? d. What is the -intercept? 9. What happens to the graph of a linear function when m is negative? 0. When m is negative, describe how ou can change m to make the line steeper, and how ou can change m to make the line flatter.. What point do all of the lines ou have graphed have in common?. Does changing m have an effect on the -intercept of the graph? 3. Predict what the graph will look like when m=0. 4. Test our prediction b graphing a line with m=0 on our calculator. Was our prediction correct? If not, what kind of line did ou get?. In our own words, describe the value of m s overall effect on the graph of a line. Activit 4.4. CT Algebra I Model Curriculum Version 3.0

22 Name: Date: Page of 6 6. Graph! =! + 0 in the calculator and sketch the graph. a. What is the slope? b. What is the value of b in the equation? c. What is the -intercept? 7. Graph! =! + in the calculator and sketch the graph. a. What changed from the graph in question (6)? b. What is the slope? c. What is the value of b in the equation? d. What is the -intercept? 8. Graph! =! + 4 in the calculator and sketch the graph. a. What changed from the graph in question (6)? b. What is the slope? c. What is the value of b in the equation? d. What is the -intercept? Activit 4.4. CT Algebra I Model Curriculum Version 3.0

23 Name: Date: Page 6 of 6 9. Graph! =! in the calculator and sketch the graph. a. What changed from the graph in question (6)? b. What is the slope? c. What is the value of b in the equation? - d. What is the -intercept? 0. If b has a negative value then the -intercept is (above, below) the -ais. Circle one answer.. If b has a positive value then the -intercept is (above, below) the -ais. Circle one answer.. What is the -intercept of the equation = + 4? 3. What is the -intercept of the equation =? 4. How does changing b in a linear function affect the graph? Be as specific as possible. Activit 4.4. CT Algebra I Model Curriculum Version 3.0

24 Name: Date: Page of 4 Trends in Bottled Water Consumption Here is a data table that shows the consumption of bottled water in the United States in the ears 000 and 007 in billions of gallons. Let s assume that during this period consumption was a linear function of time. U.S. Bottled Water Consumption Year Billions of Gallons Let represent the number of ears from 000 and represent the amount of water consumed in billions of gallons. Make a graph with on the horizontal ais and on the vertical ais b plotting the two points and using a ruler to draw a line between the two points (do not etend the line.). Find the rate of change in water consumption per ear using data for the ears 000 and Use the rate of change from question and the -intercept of our graph to write a linear equation in slope-intercept form. Activit 4.6. CT Algebra I Model Curriculum Version 3.0

25 Name: Date: Page of 4 4. Use our equation from question 3 to determine the consumption of bottled water in A more accurate figure for the consumption of bottled water in 007 is million. a. Write this large number in standard decimal notation. b. Assume that the average water bottle contains 4 ounces. Estimate the actual number of water bottles sold. Use the fact that one gallon contains 8 ounces. c. The population of the United States in 007 was about 300 million. On average how man water bottles were purchased b each person in the countr? d. In 008, bottled water consumption decreased from about 8.8 billion gallons in 007 to 8.7 billion in 008. What are some possible reasons? Activit 4.6. CT Algebra I Model Curriculum Version 3.0

26 Name: Date: Page 3 of 4 6. Here is a table that shows the consumption of bottled water in the United States from 007 to 009 in billions of gallons. As ou can see, consumption continues to decline. So from 007 to 009 we will use a new linear function to model bottled water consumption. U.S. Bottled Water Consumption Year Billions of Gallons a. As ou did in question above, let represent the number of ears from 000 and represent the amount of water consumed in billions of gallons. Make a graph with on the horizontal ais and on the vertical ais b plotting the two points and using a ruler to draw a line between the two points and etending the line to the right. b. Find the rate of change in water consumption per ear using data for the ears 007 and 009. Unlike the equation for the water consumption in question, we are not able to find the -intercept unless we do a little work. So how will we find an equation? Recall that the slope between an two points on a line is the same. c. If water consumption continues to decline at a stead rate, the slope of the line will continue to be. Activit 4.6. CT Algebra I Model Curriculum Version 3.0

27 Name: Date: Page 4 of 4 d. Use slope to count over to a third point on our line to the left of (7,8.8), and state the coordinates. e. Then find the slope between the point ou picked and the point (7,8.8). Check with a few classmates to see if ou all are getting the same slope ou found in question 6b. f. Now label an arbitrar point on our line (,). Instead of using numbers in the second point, use the variables and, because there are man different values of and on the line. g. Use the slope formula to find the slope from this arbitrar point (,) to the point (7, 8.8) and ou should still get the same slope. Wh? Here is the algebra: = m 8.8 = m( 7) 8.8 = 0.7( 7) Do a little algebra to transform the equation. Multipl both sides of the equation b 7 to bring the denominator up to the right side. Fill in the value for slope and ou will have an equation in Point-Slope form. Point-slope form simpl asserts that the slope between the fied point (7, 8.8) on the line and an arbitrar point (,) is the same slope m; in this case m =.7. h. To confirm that this equation contains the point (7, 8.8), substitute = 7 and = 8.8 into the equation 8.8 = 0.7( 7). Check to see if the result is a true statement. i. To confirm that this equation contains the point (9, 8.4), substitute = 9 and = 8.4 into the equation 8.8 = 0.7( 7). Check to see if the result is a true statement. j. Solve for to transform the equation to slope-intercept ( = m + b) form. Activit 4.6. CT Algebra I Model Curriculum Version 3.0

28 Name: Date: Page of 9 Point-Slope Form of an Equation. Graph the equation b starting at (0,4) and moving to another point on the line using the slope.. Now draw another graph of. This time pick the point ( 8, ) which is a point on the line, and use slope to count up and right from that point to find other points on the graph. Do ou end up with the same line as ou did in part a above? 3. Notice that ou can find points on a line or graph a line b starting at a point and moving according to the slope. Does it matter which point on the line is chosen to start with? Activit 4.6. CT Algebra I Model Curriculum Version 3.0

29 Name: Date: Page of 9 Facts about Point-Slope Form The point-slope form of a line is a special form that tells ou the SLOPE of a line and one POINT on the line. The point-slope formula is: m is the slope of the line; it will be a number is the coordinate of a particular point on the line, and it will be a number is the coordinate of a particular point on the line, and it will be a number is the variable is the variable Point-slope form comes from the fact that the slope between an two points on a line is alwas the same. Use the slope formula between the specific fied point (, ) and an moveable point (,): Multipl both sides of this equation b the denominator to obtain: When ou substitute the values of the specific point (, ) into the point slope formula, ou will obtain a true statement 0=0 which proves that (, ) is a point on the line. The slope-intercept form of a line is = m + b. m is the same value in both forms. Notice that it is the coefficient of the variable. EXAMPLE: For the equation, the particular point is (,7). The -coordinate of this point is and the -coordinate of this point is 7. The line has slope of. 4. Verif that (,7) is a solution to the equation b evaluating the equation when = and =7. Activit 4.6. CT Algebra I Model Curriculum Version 3.0

30 Name: Date: Page 3 of 9. For each equation in point-slope form, identif the particular point and the slope. Then graph each equation. Test our point in the equation to be sure that the point makes the equation true. a. b. Activit 4.6. CT Algebra I Model Curriculum Version 3.0

31 Name: Date: Page 4 of 9 c. d. Activit 4.6. CT Algebra I Model Curriculum Version 3.0

32 Name: Date: Page of 9 6. Use the point and the slope to write an equation of the line in point-slope form. a. (3,), m = b. (,6), c. (3,0), parallel to the line d. (0,4), perpendicular to the line e. (3,), m = 0 f. (-3,), m = g. (-,-), m=3 Activit 4.6. CT Algebra I Model Curriculum Version 3.0

33 Name: Date: Page 6 of 9 7. Plot the two points ( 3,7) and (, 3). Draw the line containing the two points. What is the slope between the two points? Write an equation in point-slope form: 8. Find an equation of the line between the given two points b first finding the slope, then finding the point-slope form of the equation. a. through points (,8) and (, 7) b. through points (, -6) and ( 7, ) Activit 4.6. CT Algebra I Model Curriculum Version 3.0

34 Name: Date: Page 7 of 9 9. This Februar and March, the middle school students had their most successful food drive, topping last ear s total b 7 items. The started the food drive on da 0 with 8 cans of fruit juice which had been donated too late to be included in the November food drive. Contributions poured in at a constant rate of food items per da. B the time the drive was over, the cans covered the cafeteria stage. a. What is the dependent variable? b. What is the independent variable? c. Find the slope described in the situation. d. Find a point described in the situation. e. Write an equation of the line in point-slope form. f. Write an equation of the line in slope-intercept form. g. Use either equation to tell how man food items had been collected b the 0 th da. h. Use either equation to tell how man das it took to collect 488 items Activit 4.6. CT Algebra I Model Curriculum Version 3.0

35 Name: Date: Page 8 of 9 Transforming a function from point-slope form into slope-intercept form 0. a. Sketch the graph of the function = 4( 3). b. Transform the previous equation into slope intercept form b appling the distributive propert on the right side and solving for. c. What are the slope and -intercept? d. Confirm that the equation in slope-intercept form gives the same graph as the equation in point-slope form. Activit 4.6. CT Algebra I Model Curriculum Version 3.0

36 Name: Date: Page 9 of 9. a. Sketch the graph of the function. b. Transform the previous equation into slope-intercept form b appling the distributive propert on the right side and solving for. c. What are the slope and -intercept? d. Confirm that the equation in slope-intercept form gives the same graph as the equation in point-slope form. Activit 4.6. CT Algebra I Model Curriculum Version 3.0

37 Name: Date: Page of 4 Finding and Using Linear Functions To do these problems, choose among the three forms of linear equations we have studied: Slope-Intercept Form:! =!" +! Standard Form: A + B = C Point-Slope Form:!!! =!(!!! ). Pedro s Parking Ticket Pedro thought he could just run into the store for a minute, so he didn t put an mone in the parking meter. He got a ticket for $ due one week later. The ticket said that it would be an additional $3.00 for each da it was paid late. a. Define the variables and write an equation that represents the total fine for an number of das late paing the ticket. b. Use the equation to find the amount Pedro must pa if he is si das late. c. When Pedro finall goes to the Town Clerk to pa the bill he has to pa $.00. How man das late was he? Activit CT Algebra I Model Curriculum Version 3.0

38 Name: Date: Page of 4. Tahira s Taicab Ride In Boston taicabs charge an initial fare and an additional amount for ever mile traveled. Tahira is having trouble figuring out how the sstem works. She paid $7.00 for a two-mile ride one da and she paid $4.0 for a nine-mile ride the net da. a. What is the independent variable? What is the dependent variable? b. Use the data given to find the amount the tais charge per mile. c. Write an equation relating the two variables. d. Use the equation to find how much a -mile taicab ride would cost. e. What is the slope and what does it mean in this situation? f. What is the initial price Tahira has to pa before she has traveled anwhere? Eplain. Activit CT Algebra I Model Curriculum Version 3.0

39 Name: Date: Page 3 of 4 3. Car Wash The Outdoor Adventure Club at Eisenhower High School needs to raise mone for their trip to Mountain Classroom, so the plan several fund raising events. The first one is a car wash. The total cost of sponges, soap, and other materials was donated b a local car dealership. The plan to charge $4.0 for each small car the wash and $8 for each large car or SUV. In the end the raised $40 for their trip. a. Define the variables and write an equation to show how the mone the raised is related to the two tpes of cars that the washed. b. What is the -intercept and what does it mean in this situation? c. What is the -intercept and what does it mean in this situation? d. What is the slope and what does it mean in this situation?. Activit CT Algebra I Model Curriculum Version 3.0

40 Name: Date: Page 4 of 4 4. Writing Equations Write equations in point-slope form, slope-intercept form, or standard form for the line that passes through each pair of points. Tr to use at least two forms of the equation for each pair. Pair of Points Point-slope form Slope-intercept form Standard form a. (, 3) and (7, 9) b. (0, 8) and (3, 0) c. (, -3) and (-3, -4) d. (-, ) and (0, 6) e. (4, 9) and (0, 9) Activit CT Algebra I Model Curriculum Version 3.0