Fair Game Review. Chapter 2. and y = 5. Evaluate the expression when x = xy 2. 4x. Evaluate the expression when a = 9 and b = 4.

Transcription

1 Name Date Chapter Fair Game Review Evaluate the epression when = and = ( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b b + ( ab ) 9. You go to the movies with five friends. Two of ou bu a ticket and a bag of popcorn. The rest of our friends bu just one ticket each. The epression + + represents the situation. Evaluate the epression when ( ) tickets cost $7. and a bag of popcorn costs $..

2 Name Date Chapter Fair Game Review (continued) Use the graph to answer the question. 0. Write the ordered pair that corresponds to Point D. F A. Write the ordered pair that corresponds to Point H. D G O. Which point is located at (, )? E C B H. Which point is located at ( 0, )?. Which point(s) are located in Quadrant IV?. Which point(s) are located in Quadrant III? Plot the point.. (, ) 7. ( 0, ) O 8. (, ) 9. (, 0) 0. (, )

3 Name Date. Graphing Linear Equations For use with Activit. Essential Question How can ou recognize a linear equation? How can ou draw its graph? ACTIVITY: Graphing a Linear Equation Work with a partner. a. Use the equation = + to complete the table. (Choose an two -values and find the -values). b. Write the two ordered pairs given b the table. These are called solution points of the equation. = + Solution Points c. PRECISION Plot the two solution points. Draw a line eactl through the two points. d. Find a different point on the line. Check that this point is a solution point of the equation = +. O e. LOGIC Do ou think it is true that an point on the line is a solution point of the equation = +? Eplain.

4 Name Date. Graphing Linear Equations (continued) f. Choose five additional -values for the table. (Choose positive and negative -values.) Plot the five corresponding solution points on the previous page. Does each point lie on the line? Solution Points = + g. LOGIC Do ou think it is true that an solution point of the equation = + is a point on the line? Eplain. h. THE MEANING OF A WORD Wh is = a + b called a linear equation? ACTIVITY: Using a Graphing Calculator Use a graphing calculator to graph = +. a. Enter the equation = + into our calculator. b. Check the settings of the viewing window. The boundaries of the graph are set b the minimum and maimum - and -values. The number of units between the tick marks are set b the - and -scales. This is the standard viewing window.

5 Name Date. Graphing Linear Equations (continued) c. Graph = + on our calculator. d. Change the settings of the viewing window to match those shown. Compare the two graphs = = + What Is Your Answer?. IN YOUR OWN WORDS How can ou recognize a linear equation? How can ou draw its graph? Write an equation that is linear. Write an equation that is not linear.. Use a graphing calculator to graph = in the standard viewing window. a. Can ou tell where the line crosses the -ais? Can ou tell where the line crosses the -ais? b. How can ou adjust the viewing window so that ou can determine where the line crosses the - and -aes?. CHOOSE TOOLS You want to graph =..8. Would ou graph it b hand or using a graphing calculator? Wh?

6 Name Date. Practice For use after Lesson. Graph the linear equation.. =. = O O Solve for. Then graph the equation.. + =. = O O. The equation = + represents the cost (in dollars) of renting a movie after das of late charges. a. Graph the equation. O b. Use the graph to determine how much it costs after das of late charges.

7 Name Date. Slope of a Line For use with Activit. Essential Question How can the slope of a line be used to describe the line? Slope is the rate of change between an two points on a line. It is the measure of the steepness of the line. To find the slope of a line, find the ratio of the change in (vertical change) to the change in (horizontal change). slope = change in change in 7 Slope = 7 ACTIVITY: Finding the Slope of a Line Work with a partner. Find the slope of each line using two methods. Method : Use the two black points. Method : Use the two gra points. Do ou get the same slope using each method? Wh do ou think this happens? a. b. c. d. 7

8 Name Date. Slope of a Line (continued) ACTIVITY: Drawing Lines with Given Slopes Work with a partner. a. Draw a line through the black point using the given slope. Draw a line through the gra point using the given slope. What do ou notice about the two lines? Slope = b. Slope = ACTIVITY: Drawing Lines with Given Slopes Work with a partner. Eamine the lines drawn through the black points in parts (a) and (b) of Activit. Draw these two lines in the same coordinate plane. Describe the angle formed b the two lines. What do ou notice about the product of the slopes of the two lines? 8

9 Name Date. Slope of a Line (continued) What Is Your Answer?. IN YOUR OWN WORDS How can the slope of a line be used to describe the line?. Based on our results in Activit, make a conjecture about two different nonvertical lines in the same plane that have the same slope.. REPEATED REASONING Repeat Activit for lines drawn through the gra points in Activit. Based on our results, make a conjecture about two lines in the same plane whose slopes have a product of. 9

10 Name Date Practice. For use after Lesson. Find the slope of the line... 9 (, ) (, 9) O O 9. (, ). (, ). The back of a moving truck is feet above the ground. A ramp etending from the back of the truck meets the ground 0 feet from the truck. What is the slope of the ramp?. Which set of stairs is more difficult to walk up? Eplain. 0 in. in. in. 8 in. Staircase 0 Staircase

11 Name Date Etension. Practice For use after Etension. Which lines are parallel? How do ou know?.. R (, ) (, ) B (0, ) (, ) (, ) (, ) G (, ) B (, ) R (, ) (, ) (, ) G (, ) Are the given lines parallel? Eplain our reasoning.. =, =. =, =. Is the quadrilateral a parallelogram? Justif our answer. A B D C

12 Name Date Etension. Practice (continued) Which lines are perpendicular? How do ou know?. (, ) 7. R (, ) (, ) (, ) B R (, ) (, ) (, 0) G B (, ) (, ) G (, ) (, ) (, ) Are the given lines perpendicular? Eplain our reasoning. 8. = 0, = 9. =, = 0. Is the parallelogram a rectangle? Justif our answer. K L J M

13 Name Date. Graphing Linear Equations in Slope-Intercept Form For use with Activit. Essential Question How can ou describe the graph of the equation = m + b? ACTIVITY: Finding Slopes and -Intercepts Work with a partner. a. Graph the equation. Find the slope of the line. Find the point where the line crosses the -ais. = + b. = + c. = d. = +

14 Name Date. Graphing Linear Equations in Slope-Intercept Form (continued) Inductive Reasoning Work with a partner. Graph each equation. Then complete the table. Equation Description of Graph Slope of Graph Point of Intersection with -ais a. = + b. = + c. = d. = +. = + 7. = = = 0. = +. =. = +

15 Name Date. Graphing Linear Equations in Slope-Intercept Form (continued) What Is Your Answer?. IN YOUR OWN WORDS How can ou describe the graph of the equation = m + b? a. How does the value of m affect the graph of the equation? b. How does the value of b affect the graph of the equation? c. Check our answers to parts (a) and (b) with three equations that are not in the table.. Wh do ou think = + m b is called the slope-intercept form of the equation of a line? Use drawings or diagrams to support our answer.

16 Name Date. Practice For use after Lesson. Find the slope and -intercept of the graph of the linear equation.. = + 9. =. + = 8 Graph the linear equation. Identif the -intercept. Use a graphing calculator to check our answer.. = +. 0 = O O. The equation = represents the time (in minutes) left after games of a tournament. a. Graph the equation. b. Interpret the -intercept and slope.

17 Name Date. Graphing Linear Equations in Standard Form For use with Activit. Essential Question How can ou describe the graph of the equation a + b = c? ACTIVITY: Using a Table to Plot Points Work with a partner. You sold a total of $ worth of tickets to a school concert. You lost track of how man of each tpe of ticket ou sold. $ Adult Number of $ Number of + = Adult Tickets Child Child Tickets $ a. Let represent the number of adult tickets. Let represent the number of child tickets. Write an equation that relates and. b. Complete the table showing the different combinations of tickets ou might have sold. Number of Adult Tickets, Number of Child Tickets, c. Plot the points from the table. Describe the pattern formed b the points d. If ou remember how man adult tickets ou sold, can ou determine how man child tickets ou sold? Eplain our reasoning

18 Name Date. Graphing Linear Equations in Standard Form (continued) ACTIVITY: Rewriting an Equation Work with a partner. You sold a total of $ worth of cheese. You forgot how man pounds of each tpe of cheese ou sold. $ Pounds of Swiss lb + $ Pounds of Cheddar lb = $ a. Let represent the number of pounds of Swiss cheese. Let represent the number of pounds of Cheddar cheese. Write an equation that relates and. b. Rewrite the equation in slope-intercept form. Then graph the equation

19 Name Date. Graphing Linear Equations in Standard Form (continued) What Is Your Answer?. IN YOUR OWN WORDS How can ou describe the graph of the equation a + b = c?. Activities and show two different methods for graphing a + b = c. Describe the two methods. Which method do ou prefer? Eplain.. Write a real-life problem that is similar to those shown in Activities and.. Wh do ou think it might be easier to graph + = 0 using standard form instead of rewriting it in slope-intercept form and then graphing? 9

20 Name Date. Practice For use after Lesson. Write the linear equation in slope-intercept form.. = 7. + =. = 0 7 Graph the linear equation using intercepts. Use a graphing calculator to check our graph.. =. + 9 = 7 O O. You go shopping and bu shirts for $ and jeans for $8. The total spent is $8. a. Write an equation in standard form that models how much mone ou spent. b. Graph the equation and interpret the intercepts. O 0

21 Name Date. Writing Equations in Slope-Intercept Form For use with Activit. Essential Question How can ou write an equation of a line when ou are given the slope and -intercept of the line? ACTIVITY: Writing Equations of Lines Work with a partner. Find the slope of each line. Find the -intercept of each line. Write an equation for each line. What do the three lines have in common? a. b. 7 c. d. 8 7

22 Name Date. Writing Equations in Slope-Intercept Form (continued) ACTIVITY: Describing a Parallelogram Work with a partner. Find the area of each parallelogram. Write an equation for each side of each parallelogram. What do ou notice about the slopes of the opposite sides of each parallelogram? a. b. 7 ACTIVITY: Interpreting the Slope and -Intercept Work with a partner. The graph shows a trip taken b a car where t is the time (in hours) and is the distance (in miles) from Phoeni. a. How far from Phoeni was the car at the beginning of the trip? Distance (miles) Car Trip t Time (hours)

23 Name Date. Writing Equations in Slope-Intercept Form (continued) b. What was the car s speed? c. How long did the trip last? d. How far from Phoeni was the car at the end of the trip? What Is Your Answer?. IN YOUR OWN WORDS How can ou write an equation of a line when ou are given the slope and -intercept of the line? Give an eample that is different from those in Activities,, and.

24 Name Date. Practice For use after Lesson. Write an equation of the line in slope-intercept form... 0 (, 9) 8 (0, 7) 8 (, 7) O O (, 8). (, ). 8 0 (, 9) 8 0 (, ) (, 8) Write an equation of the line that passes through the points.. (, 8 ), (, 8). (, ), (, ) 7. (, 0 ), (, 0) 8. You organize a garage sale. You have $0 at the beginning of the sale. You earn an average of $0 per hour. Write an equation that represents the amount of mone ou have after hours.

25 Name Date. Writing Equations in Point-Slope Form For use with Activit. Essential Question How can ou write an equation of a line when ou are given the slope and a point on the line? ACTIVITY: Writing Equations of Lines Work with a partner. Sketch the line that has the given slope and passes through the given point. Find the -intercept of the line. Write an equation of the line. a. m = b. m = c. m = d. m = 7 7

26 Name Date. Writing Equations in Point-Slope Form (continued) ACTIVITY: Developing a Formula Work with a partner. a. Draw a nonvertical line that passes,. through the point ( ) b. Plot another point on our line. Label,. This point this point as ( ) represents an other point on the line. O (, ) c. Label the rise and run of the line,.,. through the points ( ) and ( ) d. The rise can be written as. The run can be written as. Eplain wh this is true. e. Write an equation for the slope m of the line using the epressions from part (d). f. Multipl each side of the equation b the epression in the denominator. Write our result. What does this result represent?

27 Name Date. Writing Equations in Point-Slope Form (continued) ACTIVITY: Writing an Equation Work with a partner. For months, ou have saved $ a month. You now have $7 in our savings account. Draw a graph that shows the balance in our account after t months. Use our result from Activit to write an equation that represents the balance A after t months. Balance (dollars) Savings Account A t Time (months) What Is Your Answer?. Redo Activit using the formula ou found in Activit. Compare the results. What do ou notice? = is called the. The formula ou found in Activit, m( ), point-slope form of the equation of a line. Wh is = m( ), called the point-slope form? Wh do ou think this is important?. IN YOUR OWN WORDS How can ou write an equation of a line when ou are given the slope and a point on the line? Give an eample that is different from those in Activit. 7

28 Name Date. Practice For use after Lesson. Write in point-slope form an equation of the line that passes through the given point that has the given slope. ;,. m = ; (, ). m = ( ) Write in slope-intercept form an equation of the line that passes through the given points.. (, 0 ), (, ). (, 0 ), (, 0). The total cost for bowling includes the fee for shoe rental plus a fee per game. The cost of each game increases the price b $. After games, the total cost with shoe rental is $. a. Write an equation to represent the total cost to rent shoes and bowl games. b. How much is shoe rental? How is this represented in the equation? 8

29 Name Date Etension. Practice For use after Etension. Write an equation of the line that passes through the given point and is parallel to the given line. Use a graphing calculator to check our answer., ;. ( ) = +. ( ), ; = + 7, 7 ;. ( ) = +. ( ) 7, ; = Write an equation of the line that passes through the given point and is parallel to the line shown in the graph.. (, ). (, 7 ) 7. ( 0, 9) 8. (, ) 9

30 Name Date Etension. Practice (continued) Write an equation of the line that passes through the given point and is perpendicular to the given line., ; 9. ( ) = + 0. ( ), 7 ; =. (, 8 ); = 7. ( ) 8, 0 ; = + 7 Write an equation of the line that passes through the given point and is perpendicular to the line shown in the graph.. (, ). (, ). ( 0, 0 ). ( 0, ) 0

31 Name Date.7 Solving Real-Life Problems For use with Activit.7 Essential Question How can ou use a linear equation in two variables to model and solve a real-life problem? EXAMPLE: Writing a Stor Write a stor that uses the graph at the right. In our stor, interpret the slope of the line, the -intercept, and the -intercept. Make a table that shows data from the graph. Label the aes of the graph with units. Draw pictures for our stor. There are man possible stories. Here is one about a reef tank Tom works at an aquarium shop on Saturdas. One Saturda, when Tom gets to work, he is asked to clean a 7-gallon reef tank. His first job is to drain the tank. He puts a hose into the tank and starts a siphon. Tom wonders if the tank will finish draining before he leaves work. He measures the amount of water that is draining out and finds that. gallons drain out in 0 minutes. So, he figures that the rate is gallons per hour. To see when the tank will be empt, Tom makes a table and draws a graph. -intercept: number of hours to empt the tank intercept: amount of water in full tank From the table and also from the graph, Tom sees that the tank will be empt after 7 hours. This will give him hour to wash the tank before going home. Water (gallons) Time (hours)

32 Name Date.7 Solving Real-Life Problems (continued) ACTIVITY: Writing a Stor Work with a partner. Write a stor that uses the graph of a line. In our stor, interpret the slope of the line, the -intercept, and the -intercept. Make a table that shows data from the graph. Label the aes of the graph with units. Draw pictures for our stor.

33 Name Date.7 Solving Real-Life Problems (continued) ACTIVITY: Drawing Graphs Work with a partner. Describe a real-life problem that has the given rate and intercepts. Draw a line that represents the problem. a. Rate: 0 feet per second -intercept: 0 feet -intercept: seconds b. Rate: dollars per month -intercept: $00 -intercept: 8 months What Is Your Answer?. IN YOUR OWN WORDS How can ou use a linear equation in two variables to model and solve a real-life problem? List three different rates that can be represented b slopes in real-life problems.

34 Name Date.7 Practice For use after Lesson.7 Describe a real-life problem that has the given rate and intercepts. Draw a line that represents the problem.. Rate: feet per ear. Rate: pages per minute -intercept: feet -intercept: 80 pages -intercept: ears -intercept:0 minutes. You are buing shirts for an organization. You have $0 to spend. The number of short-sleeved shirts ou bu after buing long-sleeved shirts is =. +. a. Graph the equation. b. Interpret the - and -intercepts The graph relates the percent of batter life left in an MP plaer to the amount of plaing time it has left. Write an equation of the line. Batter Life Plaing Time Hours