Integrated Algebra A Notes/Homework Packet 9

Transcription

1 Name Date Integrated Algebra A Notes/Homework Packet 9 Lesson Homework Graph Using the Calculator HW # Graph with Slope/Intercept Method HW # Graph with Slope/Intercept Method-Continued HW #3 Review Put Equations into Slope-Intercept Form ( = ) HW #4 Solving for (continued) HW #5 Put Equations into Slope-Int Form and Graphing HW #6 Review for Test Test

2 Graph Using the Calculator Recall when we had to plug -values into the equation to find the -value to fill in the (,) table? Let s refresh our memories with a problem: Graph the line = + = + (, ) Well, now we are going to use the calculator to give us the values! Eample : Fill in the table and graph the line for = Press these buttons on the calculator: - = nd (tpe in the equation) - 0 GRAPH (to see the table) 3

3 Eample : Fill in the table and graph the line for = **Make sure ou use parentheses - around the when tping in the - equation, like this: 0 Y = Y = (/) + nd GRAPH 3 (to see the table) Your turn! ) Fill in the table and graph the line ) Fill in the table and graph the line for = +. for = More Review:. What is slope? What letter represents slope?. What is the -intercept? What letter represents the -intercept?

4 3. Find the slope of the line containing the points: a. (9, -) & (-, 6) b. (5, 3) & (5, -8) c. (-4, -) & (-8, 0) d. (7, -6) & (4, -6) 4. Locate the slope and -intercept in the following equations: Equation Slope -intercept a. = 3 5 b. = -9 5 c. = 7 d. = e. = Write the equation of the line with the following information: a. slope = 5, -int = -6 b. -int = 8, slope = 3 4 c. slope = -6

5 Name Date HW # For #s and, fill in the tables and graph the lines. ) = 5 ) = ) Find the slope of the line containing the points: a. (, -) and (, -5) b. (-6, -3) and (-3, ) c. (8, -3) and (4, -3) d. (-6, 3) and (0, 0) 4) Write the equation of the line with the -intercept of and the slope of 4. 5) Write the equation of the horizontal line that passes through the point (4,8). 6) Write the equation of the vertical line that passes through the point (-9, 6). 7) Simplif the following into simplest radical form: 0 54 a) b)

6 Graphing with Slope-Intercept Method There is a simple wa to graph a line, b using the slope and -intercept of the line! STEPS: Remember that in = m + b, m is the slope and b is the -intercept of the line. ) Alwas use the -intercept as our STARTING point. ) Use the slope to move from there. The top number tells ou how much to move UP or rise DOWN, and the bottom number tells ou how to move RIGHT. This is how is used! run Plot at least two more points. 3) Connect the points making a line. Be sure to label the aes and the line. Eample : Graph the line = 3 +. m = b = Step : The Starting Point is on the -ais. Put a dot here. Step : A slope of 3 means to move UP and to the RIGHT 3 from the point ou drew in Step. Do this a couple times making more points. Step 3: Connect the points. Here is our line-label it! Eample : Graph the line = + 5. m = b = Step : The Starting Point is 5 on the -ais. Put a dot here. Step : A slope of means to move DOWN and to the RIGHT from the point ou plotted in Step. Do this a couple times making points. Step 3: Connect the points & label the line.

7 Eample 3: Graph the line = 3. m = b = ***How can ou turn 3 into a fraction? Practice: 3 ) Graph the line = +. ) Graph the line = m = b = m = b = 3) Graph the line = ) Graph the line = m = b = m = b =

8 Name Date HW# ) Graph the line = +. ) Graph the line = m = b = m = b = 3) Graph the line = 3. 4) Graph the line = m = b = m = b = Review: What are the equations of these lines? [Remember HOY VUX!!!] ) )

9 Graphing with Slope-Intercept Method Continued (and mabe a couple review questions) Graph the following using the slope intercept method: m = m = 3. = 3. = = 5 4 b = b = m = b = m = 4. = 5 5. = b = 3 m = b = 6. = 4 m = b = 7. What is the equation of the vertical line through the point (9, -5)? What is the slope of this line? 8. What is the equation of the horizontal line through the point (-3, 0)? What is the slope of this line?

10 Let s do these graphs together!. = 5 3 m = b = Oh no! When we go to graph the second point, we run out of room! This is the onl time we are allowed to go LEFT! So instead of UP, RIGHT 3 we go DOWN, LEFT 3 **Now, to see if we did this correctl, look at how the left point moves to the right point [Should be UP and RIGHT 3].. = -3 4 m = b = Instead of, we go, 3. You tr! 4 = 3 5 m = b =

11 Review. Is (, -4) a solution to the equation = 6?. The point whose coordinates are (, k) lies on the line whose equation is = Find the value of k. 3. Find the slope of the line containing the points (, -4) and (-7, 5). 4. Give the slope and -intercept for each equation: Slope -intercept a. = - + b. = 7 5 c. = 3 8 d. = e. = Write the equation of the line given: Equation a. m = 4, b = -5 b. slope =, -int = c. slope = -

12 6. Graph the following equations: a. = 3 b. = 4 c. = What is the equation of the vertical line through the point (7, -4)? What is the slope of this line? 8. What is the equation of the horizontal line through the point (-6, )? What is the slope of this line? 9. Fill in the table and graph the line for =

13 Putting equations into slope-intercept form (Solve for ) One-Step Problems Recall that an equation in the format = m + b can be graphed as a line. Also, sometimes we need to solve for : ) 5 + = 5 ) + 3 = 5 Now, we are going to put these two concepts together. In order to graph a line, we want it to read =. We are going to still solve for, but there will be another variable in the equation,! STEPS (General): ) Find the and circle the entire term with it. ) Get the b itself on one side b solving the wa ou would an ordinar equation. Eample : Solve for : + 6 = 7 Remember: You can onl combine LIKE TERMS! Onl s go together and onl numbers b themselves go together! ) Circle the. ) Subtract 6 from both sides. 3) Rewrite in = m + b format. Eample : Solve for : -3 + = ) Circle the. ) Add 3 to both sides. 3) Rewrite in = m + b format. Eample 3: Solve for : = ) Circle the term with the. ) Divide everthing on both sides b. 3) Rewrite in = m + b format. Eample 4: Solve for : -3 = + 5 ) Circle the term with the. ) Divide everthing on both sides b -3. 3) Rewrite in = m + b format.

14 You might have to deal with fractions at times. Eample 5: Solve for : 8 = NOTE: It s better to leave the answer as a fraction instead of a mess decimal (for graphing purposes). If the fraction can be reduced, reduce it. [You can use Math, Frac on our calculator to reduce a fraction]. Eample 6: Solve for : - = -5-3 Practice: Solve for in all these problems. ) + = 3 ) 4 + = 6 3) = 47 4) -7 + = 6 5) 3 = + 3 6) 8 4 = - 7) -4 = + 8 8) 6 = ) 7 = 35 49

15 Name Date HW#4 Solve the following equations for : ) 3 = 7 ) + = 5 3) -3 = ) 4 = 3 5) 5 = 0 9 6) = Review: ) a) Solve for : 4 + = + 8 b) Show our CHECK here: ) A building casts a shadow of meters along level ground. The ras of the sun hit the ground at a 4º angle. What is the height of the building (to the nearest tenth of a meter)?

16 Solving for Mulit-Step Problems Warm-up: Solve for. a. - 5= 4 b. 3 = c. 9 = You might have to do more than one step to get b itself. Be careful with signs and combining like terms. Eample : Solve for = 35 Eample : Solve for. 4 = 3 Eample 3: Solve for = 0 Eample 4: Solve for = 4 Eample 5: Solve for =

17 Practice: Solve for in these problems. ) + = 43 ) - + = 66 3) 5 = ) 6 = + 8 5) 6 8 = -3 6) = 7) = 0 8) 4 = 5 Challenge: Solve for : + = 7 3