Additional Practice
Additional Practice ACTIVITY 3.1 Look at each of the following graphs. What do you notice about the relationship between x and y? 1.
y 10
c. x 2
6
d. x - 6
2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4 -6
7. Give an example of an expression that represents a linear pattern and an example of an expression that represents a nonlinear pattern. What makes a pattern linear? ACTIVITY 3.2
-8 -10
2.
6. Determine which of the following expressions displays a linear relationship. Use multiple representations to explain your reasoning. 2x a. __ 3 b. 4 + 0.2x
8 4
Find the domain and range for each of the following sets of data. 8. {(11, 2), (2, 14), (-5, 13), (58, 33)}
y
9.
10 8 6 4 2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4 © 2010 College Board. All rights reserved.
UNIT 3
-6 -8 -10
x
y
2 4 6 8
5 -6 3 -8
Determine if the relations in Items 10–15 represent functions. Explain your reasoning. 10. {(2, 4), (-6, 5), (1, 0), (4, 2), (0, -1)} 11.
Graph the following data sets and identify each as linear or nonlinear. 3. {(4, 2), (6, 2), (-3, 2), (-2, 2)} 4. {(0, 0), (-1, 1), (1, 1), (-2, 4)} 5. {(-2, 1), (0, 5), (2, 9), (-4, -3)}
x
y
-2 3 -2 9
6 9 4 3
Level 3, Unit 3 • Equations and the Coordinate Plane
1
Additional Practice
12. y = x + 4 for x = 1, 2, 3, 4
ACTIVITY 3.3
13.
Brynn rides her bike 42 miles in 2 hours.
y
16. Create a ratio of Brynn’s miles per hour.
10
17. Using the ratio you found in Item 16, determine how far Brynn can ride in 6 hours.
8 6 4 2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
19. Find the slope and y-intercept of the following.
-4 -6 -8
a.
-10
14.
18. If Brynn rode her bike for 57 miles at the rate you found, how long was she riding?
y 10 8
x
y
2 1 0
10 7 4
b.
6 4
y 10
2 -10 -8 -6 -4 -2
-2
8 2
4
6
8 10
x
6 4
-4
2
-6
-10 -8 -6 -4 -2
-8 -10
-2
2
4
6
8 10
x
-4 -6 -8
15.
y
-10
10 8 6 4 2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4 -6 -8 -10
2
SpringBoard® Mathematics with MeaningTM Level 3
3 contains the 20. If a line with a slope of __ 4 point with coordinates (-1, 4), give the coordinates of 3 other points that must also be on the line.
© 2010 College Board. All rights reserved.
UNIT 3
Additional Practice ACTIVITY 3.4 21. Find the slope of the line that contains the coordinates shown in the table. x
y
3 4 5
1 1.5 2
30. Write an equation for the line graphed below. y 10 8 6 4 2
Graph the following linear equations.
-10 -8 -6 -4 -2
22. y = -3x 23. y = 5x 1x 24. y = __ 4 25. A line with a slope of 3 goes through the point (-2, -4). It also goes through the point (0, p). What is the value of p? 26. Write the equation of the line graphed below.
6
x
8 10
-6 -8 -10
ACTIVITY 3.5
y 10
8
8
6
6
4
4
2
© 2010 College Board. All rights reserved.
4
-4
31.
10
-2
2
-2
Find the x- and y-intercepts of the following graphs.
y
-10 -8 -6 -4 -2
UNIT 3
2
4
6
8 10
-4 -6 -8 -10
2
x -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4 -6 -8 -10
Graph the following linear equations. 27. y = 4x - 3 28. y = -5x + 4 4x + 2 29. y = __ 3
Level 3, Unit 3 • Equations and the Coordinate Plane
3
UNIT 3
Additional Practice
32.
Write the equation of the lines graphed below.
y 10
41.
8 6
y 10
4
8
2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
6
x
4 2
-4 -10 -8 -6 -4 -2
-6 -8
-2
2
4
6
8 10
2
4
6
8 10
x
-4
-10
-6 -8
42.
y 10
35. y = 3x - 9 36. 8x + y = 8
8
Graph the line with the given intercepts.
2
37. x-intercept: 4 y-intercept: -3 38. x-intercept: -2 y-intercept: 5 Graph the following linear equations. 39. x = 4 40. y = -7
4
SpringBoard® Mathematics with MeaningTM Level 3
6 4
-10 -8 -6 -4 -2
-2
x
-4 -6 -8 -10 © 2010 College Board. All rights reserved.
Find the x- and y-intercepts of the line with the following equations. 33. y = 5x + 25 34. y = -2x + 8
-10
Additional Practice ACTIVITY 3.6 Determine if the graphs below have a positive association, a negative association, or no association. 43.
y
46. Find the equations of the trend lines for any of the graphs in questions 43−45 that have a positive or negative association. ACTIVITY 3.7 47. Determine which of the following points are solutions to the system of equations below.
10
{(2, 4), (6, 8), (2, -4), (-6, 8)}
8 6
{ 2x5x ++ 3yy ==-4-6
4 2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4
48. Determine which of the following points are solutions to the system of equations below. {(0, 4), (5, -7), (1, 3),(-4, 2)}
-6
{ 4x6x +- 2yy ==70
-8 -10
44.
Solve the following systems of equations by graphing. y = 6x + 4 49. y = -2x + 4
y
{ -3x + y = -6 50. { -6x + 2y = 5
10 8 6 4 2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
© 2010 College Board. All rights reserved.
-4
Solve the following systems of equations algebraically. y = 2x + 4 51. y = x - 5
{
-6 -8
{
1x y = __ 52. 4x +22y = 20
-10
45.
UNIT 3
y
{
x - 3y = 12 53. -x + 2y = -15
10 8 6 4 2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4 -6 -8 -10
Level 3, Unit 3 • Equations and the Coordinate Plane
5
y 10
c. x 2
6
d. x - 6
2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4 -6
7. Give an example of an expression that represents a linear pattern and an example of an expression that represents a nonlinear pattern. What makes a pattern linear? ACTIVITY 3.2
-8 -10
2.
6. Determine which of the following expressions displays a linear relationship. Use multiple representations to explain your reasoning. 2x a. __ 3 b. 4 + 0.2x
8 4
Find the domain and range for each of the following sets of data. 8. {(11, 2), (2, 14), (-5, 13), (58, 33)}
y
9.
10 8 6 4 2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4 © 2010 College Board. All rights reserved.
UNIT 3
-6 -8 -10
x
y
2 4 6 8
5 -6 3 -8
Determine if the relations in Items 10–15 represent functions. Explain your reasoning. 10. {(2, 4), (-6, 5), (1, 0), (4, 2), (0, -1)} 11.
Graph the following data sets and identify each as linear or nonlinear. 3. {(4, 2), (6, 2), (-3, 2), (-2, 2)} 4. {(0, 0), (-1, 1), (1, 1), (-2, 4)} 5. {(-2, 1), (0, 5), (2, 9), (-4, -3)}
x
y
-2 3 -2 9
6 9 4 3
Level 3, Unit 3 • Equations and the Coordinate Plane
1
Additional Practice
12. y = x + 4 for x = 1, 2, 3, 4
ACTIVITY 3.3
13.
Brynn rides her bike 42 miles in 2 hours.
y
16. Create a ratio of Brynn’s miles per hour.
10
17. Using the ratio you found in Item 16, determine how far Brynn can ride in 6 hours.
8 6 4 2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
19. Find the slope and y-intercept of the following.
-4 -6 -8
a.
-10
14.
18. If Brynn rode her bike for 57 miles at the rate you found, how long was she riding?
y 10 8
x
y
2 1 0
10 7 4
b.
6 4
y 10
2 -10 -8 -6 -4 -2
-2
8 2
4
6
8 10
x
6 4
-4
2
-6
-10 -8 -6 -4 -2
-8 -10
-2
2
4
6
8 10
x
-4 -6 -8
15.
y
-10
10 8 6 4 2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4 -6 -8 -10
2
SpringBoard® Mathematics with MeaningTM Level 3
3 contains the 20. If a line with a slope of __ 4 point with coordinates (-1, 4), give the coordinates of 3 other points that must also be on the line.
© 2010 College Board. All rights reserved.
UNIT 3
Additional Practice ACTIVITY 3.4 21. Find the slope of the line that contains the coordinates shown in the table. x
y
3 4 5
1 1.5 2
30. Write an equation for the line graphed below. y 10 8 6 4 2
Graph the following linear equations.
-10 -8 -6 -4 -2
22. y = -3x 23. y = 5x 1x 24. y = __ 4 25. A line with a slope of 3 goes through the point (-2, -4). It also goes through the point (0, p). What is the value of p? 26. Write the equation of the line graphed below.
6
x
8 10
-6 -8 -10
ACTIVITY 3.5
y 10
8
8
6
6
4
4
2
© 2010 College Board. All rights reserved.
4
-4
31.
10
-2
2
-2
Find the x- and y-intercepts of the following graphs.
y
-10 -8 -6 -4 -2
UNIT 3
2
4
6
8 10
-4 -6 -8 -10
2
x -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4 -6 -8 -10
Graph the following linear equations. 27. y = 4x - 3 28. y = -5x + 4 4x + 2 29. y = __ 3
Level 3, Unit 3 • Equations and the Coordinate Plane
3
UNIT 3
Additional Practice
32.
Write the equation of the lines graphed below.
y 10
41.
8 6
y 10
4
8
2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
6
x
4 2
-4 -10 -8 -6 -4 -2
-6 -8
-2
2
4
6
8 10
2
4
6
8 10
x
-4
-10
-6 -8
42.
y 10
35. y = 3x - 9 36. 8x + y = 8
8
Graph the line with the given intercepts.
2
37. x-intercept: 4 y-intercept: -3 38. x-intercept: -2 y-intercept: 5 Graph the following linear equations. 39. x = 4 40. y = -7
4
SpringBoard® Mathematics with MeaningTM Level 3
6 4
-10 -8 -6 -4 -2
-2
x
-4 -6 -8 -10 © 2010 College Board. All rights reserved.
Find the x- and y-intercepts of the line with the following equations. 33. y = 5x + 25 34. y = -2x + 8
-10
Additional Practice ACTIVITY 3.6 Determine if the graphs below have a positive association, a negative association, or no association. 43.
y
46. Find the equations of the trend lines for any of the graphs in questions 43−45 that have a positive or negative association. ACTIVITY 3.7 47. Determine which of the following points are solutions to the system of equations below.
10
{(2, 4), (6, 8), (2, -4), (-6, 8)}
8 6
{ 2x5x ++ 3yy ==-4-6
4 2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4
48. Determine which of the following points are solutions to the system of equations below. {(0, 4), (5, -7), (1, 3),(-4, 2)}
-6
{ 4x6x +- 2yy ==70
-8 -10
44.
Solve the following systems of equations by graphing. y = 6x + 4 49. y = -2x + 4
y
{ -3x + y = -6 50. { -6x + 2y = 5
10 8 6 4 2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
© 2010 College Board. All rights reserved.
-4
Solve the following systems of equations algebraically. y = 2x + 4 51. y = x - 5
{
-6 -8
{
1x y = __ 52. 4x +22y = 20
-10
45.
UNIT 3
y
{
x - 3y = 12 53. -x + 2y = -15
10 8 6 4 2 -10 -8 -6 -4 -2
-2
2
4
6
8 10
x
-4 -6 -8 -10
Level 3, Unit 3 • Equations and the Coordinate Plane
5
