Equation of a Line

1. A marble will be randomly selected from a bag of solid-colored marbles. The probability of selecting a red marble is 5/19. The probability of selecting a blue marble is 4/19. What is the probability of selecting a red marble or a blue marble?

2017 December(A10) Math Question 1

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

4. For RT ↔ shown below, point S is on RT , the length of RS is 8 cm, and the length of ST is 18 cm. What is the distance, in centimeters, between T and the midpoint of RS ?

Distance formula (distance between 2 points, vertical distance, horizontal distance)

2020 December(D03) Math Question 4

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

5. For ↔RT shown below, point S is on RT, the length of RS is 10 cm, and the length of ST is 18 cm. What is the distance, in centimeters, between T and the midpoint of RS ?

2021 April(D05) Math Question 5

6. Ming purchased a car that had a purchase price of $5,400, which included all other costs and tax. She paid $1,000 as a down payment and got a loan for the rest of the purchase price. Ming paid off the loan by making 28 payments of $200 each. The total of all her payments, including the down payment, was how much more than the car's purchase price?

2017 December(A10) Math Question 6

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

2018 April(A09) Math Question 6

8. When points A and B(-3,4) are graphed in the standard (x,y) coordinate plane below, the midpoint of AB will be (1,2). What will be the coordinates of point A ?

2015 June(73C) Math Question 8

9. In the standard (x,y) coordinate plane, what is the midpoint of the line segment that has endpoints (3,8) and (1,-4) ?

2017 April(74F) Math Question 9

9. On a bike trail there 'are 5 2heckpoints numbered in
order, Checkpoint 1 through Checkpoint 5,.as shown in
the figure below. Some di!ltances along the trail
between 2 checkpoints are given: 6.6 miles between
1 and 3; 4.5 miles between 2 and 3; and 9.7 miles
betwe~ri 2 and 5. Which .of the following values is
closest to the distance, in miles, along the tr.ail between
Checkpoint 1 and Checkpoint 5 ?

2019 June(B02) Math Question 9

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. On the real number line, point J is at —7 and point K is at —14. What is the distance between J and K ?

2015 April(73G) 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

2019 June(72F) Math Question 11

2018 December(B05) Math Question 12

2009 December(68A) Math Question 12

12. In the standard (x,y) coordinate plane, the point (2,1) is the midpoint of CD. Point  C has coordinates (6,8). What are the coordinates of point D ?

2021 April(Z04) 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

13. In the standard (x,y) coordinate plane, the point (3,-7) is the midpoint of the line segment with endpoints (9, -11) and:

2018 April(A09) Math Question 13

2019 April(Z15) Math Question 13

2009 December(68A) Math Question 13

13. Which of the following (x,y) pairs is the solution for the system of equations x + 2y = 2 and —2x + y = 16 ?

2017 December(A10) Math Question 13

2012 April(70G) 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

15. The straight-line distance, in miles, from Marville to Bright City must be:

2014 April(71H) 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

2012 June(70C) 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

2019 December(C03) Math Question 17

2013 December(71E) Math Question 17

17. In the standard (x,y) coordinate plane, the midpoint of AB is at (2,1), and A is at (8,10). What is the x-coordinate of B ?

2018 June(A11) 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

2011 June(69F) Math Question 19

19. In the standard (x,y) coordinate plane, the point (2,-4) is the midpoint of the line segment with endpoints (8,-8) and:

2015 April(73G) 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

2009 December(68A) Math Question 21

2020 July(C01) 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. For AC shown below, B is on AC, the length of AB is 12 cm, and the length of BC is 20 cm. What is the distance, in centimeters, between C and the midpoint

2013 June(71C) 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

22. As shown below, A, B, C, and D are collinear, with B between A and C and with C between B and D. Given AC = BD = 12 cm and given BC = 3 cm, what is AD, in centimeters?

2016 April(73E) Math Question 22

2009 December(68A) Math Question 23

2010 June(68C) Math Question 24

2009 June(67C) Math Question 24

2020 July(C01) Math Question 24

24. What rational number is exactly halfway between 3/16 and 7/32 on the real number line?

Number Line

2021 April(D05) Math Question 24

24. What is the length, in coordinate units, of the line segment with endpoints (-8,4) and (4,9) in the standard (x,y) coordinate plane?

2015 December(72E) 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

2011 April(67F) Math Question 28

28. On Friday night, the Morrison family set up camp in the Ocala National Forest. On Saturday morning they hiked to a wilderness area 3 miles due north and 4 miles due east of their campsite. The elevation of the wilderness area is the same as the elevation of the campsite. To the nearest 0.1 mile, what is the straight-line distance from the wilderness area to the Morrisons' campsite?

2016 April(73E) Math Question 28

28. In the standard (x,y) coordinate plane, what is the distance, in coordinate units, from A(5 1/3,-3) to B(-1 5/9 ,−3) ?

2020 December(D03) 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

30. What is the distance, in coordinate units, from B to D ?

2017 June(74C) Math Question 30

2010 December(69A) Math Question 31

2019 December(C03) Math Question 31

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

34. Whatis the length of AB in coordinate units?

2019 June(B02) Math Question 34

34. What rational number is exactly halfway between and on the real number line?

Midpoint Formula

2020 December(D03) Math Question 34

35. When considering the changing triangle formed by A, B, and the moving airplane (C), which of the angles below increases in measure as the airplane flies due west beyond the point directly above A ?

2017 December(A10) Math Question 35

35. Students and adults from Western High School visited an amusement park on a field trip. The amusement park charged $25 for each adult ticket and $20 for each student ticket. Before the trip, the students were given this information about the Happy Dragon roller coaster: the average speed of the roller coaster is 50 miles per hour, and 1 ride on the roller coaster track is completed in 2.25 minutes. A graph showing the height above level ground, in feet, with respect to the time into the ride, in seconds, is given below. Which of the following values is closest to the total distance traveled, in miles, during 1. complete ride on the roller coaster track?

2018 April(A09) Math Question 35

2013 December(71E) Math Question 35

2013 April(71G) Math Question 35

2010 December(69A) 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?

Equation of a LineThere are 162 ACT math questions under Equation of a Line

Sub-topics

2017 December(A10) Math Question 1

2018 April(A09) Math Question 1