Equation of a Line

Equations that Describe a Line

1. A line in the standard (x,y) coordinate plane passes through the points (-2,-6) and (5,3). The slope of the line:

2018 April(A09) Math Question 1

Wally buys dog collars online for $4 each. The shipping and handling fee is $5 total, regardless of the number of dog collars ordered. Which of the following equations represents the relationship between x, the number of dog collars ordered, and y, Wally's total bill in dollars?

2024 April(Z13) Math Question 3

5. A line in the standard (x,y) coordinate plane passes through the points (-3,4) and (2,-5). The slope of the line:

2015 June(73C) Math Question 5

6. What is the slope-intercept form of 9x — y 5 = 0 ?

2018 April(A09) Math Question 6

9. What is the slope of the line given by the equation 2x + 7y = —12 ?

2014 December(72G) Math Question 9

A line in the standard (x,y) coordinate plane passes through the point (3,4). The slope of the line:

35 February(Z14) Math Question 9

2019 December(C03) Math Question 10

10. In the standard (x,y) coordinate plane, what is the slope of the line through (−3,1) and (5,6) ?

Slope

2021 December(E23) Math Question 10

The scales on both axes of the standard (x,y) coordinate plane below are the same. Of the following values, which one is the best estimate for the slope of the line graphed in the plane?

2023 September(G01) Math Question 10

11. In the standard (x,y) coordinate plane, what is the slope of the line 4x + 7y = 9 ?

2018 June(A11) Math Question 11

11. What is the slope of the line through (-2,1) and (2,-5) in the standard (x,y) coordinate plane?

2017 April(74F) Math Question 11

2020 June(C02) Math Question 11

2018 December(B05) Math Question 12

2009 December(68A) Math Question 12

In the standard (x,y) coordinate plane, a line intersects the y-axis at (0,3) and contains the point (9,4). What is the slope of the line?

2023 April(F11) Math Question 12

2019 April(Z15) Math Question 13

15. In the standard (x,y) coordinate plane below, 5 points are labeled on a parabola. Which of the following lines has the slope of least value?

2016 April(73E) Math Question 15

2019 June(72F) Math Question 16

2011 April(67F) Math Question 16

16. Consider the line 3x − 4y = 6 in the standard (x,y) coordinate plane. For the point on this line with x-coordinate equal to 3, what is the y-coordinate?

Equation of Line

2021 April(D05) Math Question 16

17. In the standard (x,y) coordinate plane, what is the slope of the line given by the equation 4x = 7y + 5 ?

2017 April(74F) Math Question 17

2009 April(66F) Math Question 17

18. In the standard (x,y) coordinate plane, the line represented by which of the following equations goes through (0,7) and is parallel to the line represented by y = —2x — 4 ?

2016 December(74H) Math Question 18

18. In the standard (x1y) cootdmate plane, what is the siope
of the line given by the equation 5x = 9y + 18 ?

2019 June(B02) Math Question 18

19. One of the following equations represents the line
gra)?hed jn the ,standard (x,y) coordinate plane below.
Wfilch one?,

2019 June(B02) Math Question 19

2020 June(C02) Math Question 19

19. The line with equation 2x + 5y = 9 is graphed in the standard (x,y) coordinate plane. What is the slope of the line?

2020 December(D03) Math Question 19

19. In the standard (x,y) coordinate plane, a line intersects the y-axis at (0,2) and contains the point (8,5). What is the slope of the line?

2021 April(D05) Math Question 19

2011 April(67F) Math Question 20

21. Which of the following transformations shifts all points graphed in the standard (x,y) coordinate. plane down 5 coordinate units?

2013 June(71C) Math Question 21

2018 December(B05) Math Question 21

What is the slope of the line passing through the points (−1,4) and (2,−1) in the standard (x,y) coordinate plane?

2023 September(G01) Math Question 21

One of the following equations represents the line of best fit shown in the scatterplot below. Which one?

2024 September(H11) Math Question 21

2012 June(70C) Math Question 22

2010 June(68C) Math Question 22

22. What is the slope of a line, in the standard (x,y) coordinate plane, that is parallel to x + 5y = 9 ?

2021 April(Z04) Math Question 22

2009 December(68A) Math Question 23

2009 June(67C) Math Question 24

2020 July(C01) Math Question 24

The cost of a hotel room, y dollars, based on the rating, x, provided by a travel agency is modeled by the linear equation y = 2.34x + 67.75. Which of the following statements describes the rate of change of this model?

2023 September(G01) Math Question 24

2012 April(70G) Math Question 26

2009 April(66F) Math Question 26

2011 June(69F) Math Question 26

2020 June(C02) Math Question 26

26. Which of the following equations represents the line in the standard (x,y) coordinate plane that passes through (2,-3) and has a slope of —1/2 ?

2016 April(73E) Math Question 26

27. When 6x = 2y - 18 is graphed in the standard (x,y) coordinate plane, what is the y-intercept?

2013 June(71C) Math Question 27

2019 April(Z15) Math Question 27

2012 December(71A) Math Question 28

29. The side view of the pool is placed in the standard (x,y) coordinate plane, keeping the same orientation and scale, such that both vertical segments showing depth are parallel to the y-axis. Which of the following values is closest to the slope of the line segment connecting the shallow end to the deep end?

2018 June(A11) Math Question 29

2011 June(69F) Math Question 29

29. In the standard (x,y) coordinate plane, what is the slope of the line through (3,7) and (-2,4) ?

2014 April(71H) Math Question 29

The following linear functions are defined either with an equation, a graph, or a table of values. Which of the following functions has the greatest slope?

2024 June(G20) Math Question 33

2013 April(71G) Math Question 34

2009 June(67C) Math Question 34

2013 December(71E) Math Question 35

2013 April(71G) Math Question 35

35. What is the slope of the line that passes through the points (-2,5) and (3,-4) in the standard (x,y) coordinate plane?

2013 June(71C) Math Question 35

35. Which of the following is an equ'ation of AB ?

2019 June(B02) Math Question 35

Two perpendicular lines in the standard (x,y) coordinate plane each have nonzero slopes. What is the product of their slopes?

2025 October(J08) Math Question 35

Which of the following values is closest to the slope of the line of best fit (with the least sum of squared residuals) for the data represented by the scatterplot in the standard (x,y) coordinate plane below?

2024 December(H31) Math Question 35

2010 June(68C) Math Question 36

36. Malik will spend a total of $30.00 before sales tax on x bags of marbles and y cars purchased at the prices shown on the partial receipt. One of the following line segments graphed in the standard (x,y) coordinate plane contains points for all possible combinations of x and y. Which one?

2021 December(E23) Math Question 36

37. Which of the following values is closest to the average slope, in feet per second, of the graph on the interval between 40 seconds and 90 seconds?

2018 April(A09) Math Question 37

37. A line in the standard (x,y) coordinate plane is parallel to the x-axis and 6 coordinate units above it. Which of the following is an equation of this line?

2014 April(71H) Math Question 37

2012 June(70C) Math Question 37

2011 June(69F) Math Question 39

40. Trapezoid ABCD is graphed in the standard (x,y) coordinate plane below. What is the slope of CD ?

2014 June(72C) Math Question 40

41. In the standard (x,y) coordinate plane below, R is located at (1,0), S is located at (1,2), and T is located at (4,0) to form right triangle ❑RST The given lengths are in coordinate units. What is the slope of ST ?

2015 December(72E) Math Question 41

42. In the standard (x,y) coordinate plane, what is the slope of the line that is perpendicular to the line 8x + 7y = 112?

2015 April(73G) Math Question 42

2012 April(70G) Math Question 42

43. Three linear equations are given below. y= x y= x + 1 y = —x + 1 In terms of being parallel, being perpendicular, or intersecting, how are the graphs of these equations related in the standard (x,y) coordinate plane?

2014 December(72G) Math Question 43

2020 July(C01) Math Question 43

2013 December(71E) Math Question 43

44. In the standard (x,v) coordinate plane, the coordinates of the y-intercept of the graph of the function v = f(x) are (0,-2). What are the coordinates of the v-intercept of the graph of the function y = f(x) — 3 ?

2018 April(A09) Math Question 44

2009 December(68A) Math Question 44

What are the slope and y-intercept of the line that goes through (0,8) and (4/3, 0) in the standard (x,y) coordinate plane?

2024 September(H11) Math Question 44

2012 April(70G) Math Question 45

45. In the standard (x,y) coordinate plane, the 3 lines with equations y= _3_x−3, y=−_2_x+2, and x=0 bound a triangular region. What is the area, in square coordinate units, of that triangular region? (A blank grid has been provided for your use.)

2021 June(D06) Math Question 45

45. During a snowstorm, the relationship between the depth of accumulated snow, y inches, and the elapsed time, x hours, was modeled by the equation 2x — 5y = —5. One of the following graphs in the standard (x,y) coordinate plane models the equation for positive values of x and y. Which one?

2015 June(73C) Math Question 45

47. In the standard (x,y) coordinate plane, which of the following lines is perpendicular to the line 3y = 4x + 2 ?

2015 December(72E) Math Question 47

2013 December(71E) Math Question 47

48. In the standard (x,y) coordinate plane, what is the slope of a line that is perpendicular to 2x — 3y = 9 ?

2014 April(71H) Math Question 48

2010 April(68G) Math Question 48

49. Point M will remain fixed, and point Q will move to the right along the x-axis. As Q continues to move to the right, which of the following statements describes what will happen to the slope of MQ ____ ?

2021 April(Z04) Math Question 49

50. In the standard (x,y) coordinate plane, line a contains the points (-4,2) and (-1,-3), and line b contains the points (3,0) and (7,0). At what point does line a intersect line b ?

2014 June(72C) Math Question 50

2010 December(69A) Math Question 51

2019 June(72F) Math Question 52

54. Experimental data is represented in the standard (x,y) coordinate plane by a scatterplot consisting of 6 points: (1, 1.4), (2, 2.9), (3, 3.4), (4, 3.1), (5, 1.9), and (6, 0.2). When all possible real values for a, b, and c are considered, which of the following functions best fits the experimental data?

2014 April(71H) Math Question 54

54. In the standard (x,y) coordinate plane below, the line through the points (-2,0) and (0,-4) is graphed. Which of the following values is the slope of any line that is in this plane and is perpendicular to the graphed line?

2015 June(73C) Math Question 54

2013 December(71E) Math Question 55

55. In the standard (x,y) coordinate plane below, a shaded square is shown with vertices at (2,3), (2,4), (3,3), and (3,4). Two  lines, y = rx and y = sx, each intersect the shaded square at exactly 1 point. Given that r ≠ s, what is the positive difference of r and s ?

2021 April(D05) Math Question 55

Which of the following values is closest to the average rate of change of Shakir's typing speed, in words per minute per day, from the 1st day of class to the 99th day of class?

2024 December(H31) Math Question 55

A straight line through the point with (x,y) coordinates (−1,1) has slope 2 and contains the point (3,d). What is the value of d?

2024 December(H31) Math Question 57

59. In the standard (x,y) coordinate plane, what is the
y-intercept of the graph of the function y =f(x) defined below?

2019 June(B02) Math Question 59

59. In the standard (x,y) coordinate plane below, lines q, r, and s all have an x-intercept of —4. The slope of line q is 1, the slope of line r is 2/3, and the slope of line s is the average of the slopes of lines q and r. What is the y-intercept of line s?

Equations that Describe a LineEquation of a LineACT math questions

2018 April(A09) Math Question 1

2024 April(Z13) Math Question 3