Slope Questions for the ACT
Instructions: Try the ACT slope questions below. The answers are given in the next section. The formulas are given after the last question.
1. Consider a line that crosses the y axis at 10 and upon which point (6, 4) lies. What is the slope of this line?
2. The measurements of a hill can be placed on a two dimensional linear graph on which x = 5 and y = 165. If the line crosses the y axis at 15, what is the slope of this hill?
3. What is the point slope formula for a line that includes the following points: (-5, 4) and (7, -8)?
4. What is the equation of a line that passes through point (x,y) and has a slope of -2 and a y-intercept of 6?
5. What is the slope of a line that passes through point (2, 4) and a y-intercept of -4?
Slope for ACT Math
Calculating slope is one of the most important skills that you will need for coordinate geometry problems on your ACT test. You will need these slope formulas for the exam:
Slope formula: m = (y2 – y1)/ (x2 – x1)
Slope-intercept form: y = mx + b ( where m = slope; b = y intercept; and x and y are points on the graph)
Point-slope form: (y – y1) = m(x – x1)
Equation of a line: y = mx + b
The slope-intercept form is sometimes referred to as the equation of a line. Remember that m is the slope and b is the y intercept.
Answers to the Slope Questions
Problem 1 – The correct answer is -1.
y = mx + b [m =slope and b = y-intercept]
The line crosses the y axis at 10 and includes point (6, 4).
We have got point (6, 4), so we can substitute those values for x and y.
4 = m6 + b
Then put in 10 for the y-intercept to solve.
4 = m6 + 10
4 − 10 = m6 + 10 − 10
− 6 = m6
− 1 = m
Problem 2 – The correct answer is 30.
The line includes point (5, 165) and crosses the y axis at 15. So, put these values into the formula to solve.
y = mx + b [m = slope and b = y intercept]
165 = m5 + 15
165 − 15 = m5 + 15 − 15
150 = m5
150 ÷ 5 = m5 ÷ 5
30 = m
Problem 3 – The correct answer is (-5 – 7) = m(4 – -8)
The question is asking for the point slope formula for a line that crosses points (-5, 4) and (7, -8).
Put values into the formula to solve.
Point-slope form: (y – y1) = m(x – x1)
(-5- 7) = m(4 – -8)
Problem 4 – The correct answer is y = -2x + 6
The line goes through point (x, y), has a slope of -2, and a y-intercept of 6.
y = mx + b [m = slope and b = y intercept]
y = -2x + 6
Problem 5 – The correct answer is 4.
The line passes through points (2, 4) and (0, -4)
m = (y2 – y1)/ (x2 – x1)
m = (-4 – 4)/ (0 – 2)
m = -8/-2
m = 4
More math help
Have a look at our geometry problems.
Go ahead and try our free sample ACT math test.
