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ACT Linear equations practice questions

Linear equations sits in the Algebra reporting category on the ACT Math section. Prep36 has 11 questions tagged to this skill, every one with a worked explanation. Three of them are below in full, with the reasoning, so you can see what the skill actually looks like before you practise it.

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What Linear equations covers on the ACT

Within this skill the Prep36 bank covers solving with distribution, slope from two points, two-step equation in one variable, linear equation with variables on both sides, finding an x-intercept and parallel lines in slope-intercept form.

Math is 45 questions in 50 minutes, which is about 66 seconds each, and it is one of the three sections that average into your composite. The difficulty split across the 11 questions tagged here is 8 easier, 3 medium and 0 harder.

Questions are original, written to the Enhanced ACT format. Prep36 is not affiliated with ACT, Inc.

3 linear equations questions, with the reasoning

Question 1 easy

What is the solution to the equation 5(x - 3) = 2x + 6 ?

  1. A. x = -3
  2. B. x = 3
  3. C. x = 7 correct
  4. D. x = 21
Why: Distribute first: 5(x - 3) = 5x - 15, so the equation is 5x - 15 = 2x + 6. Subtract 2x to get 3x - 15 = 6, add 15 to get 3x = 21, and divide by 3 for x = 7. The value 21 is what you get by stopping one step early at 3x = 21, and 3 comes from distributing the 5 to the x only and writing 5x - 3 = 2x + 6. Plugging 7 back in confirms it: 5(4) = 20 and 2(7) + 6 = 20.Tip: after you isolate the variable term, ask yourself whether the variable is still carrying a coefficient. If it is, you have one division left to do.
Question 2 medium

A line in the standard (x, y) coordinate plane passes through the points (-2, 5) and (4, -7). Which equation represents this line?

  1. A. y = -2x - 7
  2. B. y = -2x + 1 correct
  3. C. y = -(1/2)x + 4
  4. D. y = 2x + 9
Why: Slope is the change in y over the change in x, taken in the same order for both: (-7 - 5)/(4 - (-2)) = -12/6 = -2. Substitute (-2, 5) into y = -2x + b to get 5 = 4 + b, so b = 1 and the line is y = -2x + 1. Verify with the second point: -2(4) + 1 = -7, which matches. The choice y = 2x + 9 comes from subtracting the coordinates in mismatched orders, which flips the slope's sign, and y = -2x - 7 has the right slope with the y-intercept solved incorrectly.Tip: once you have a candidate line, plug in the point you did not use to build it. If both given points satisfy the equation, you are done.
Question 3 easy

What is the slope of the line that passes through the points (1, -4) and (5, 8) in the standard (x,y) coordinate plane?

  1. A. 1/3
  2. B. 3 correct
  3. C. -3
  4. D. 12
Why: Slope is the change in y over the change in x, which is (8 - (-4)) / (5 - 1) = 12/4 = 3. The choice 1/3 inverts the fraction by dividing the run by the rise, 12 stops at the numerator without dividing, and -3 mishandles the double negative in 8 - (-4). Tip: as x increases the y value here rises, so the slope must be positive, which eliminates a negative choice immediately.

The explanation is the point. Getting a question wrong tells you nothing you did not already suspect; knowing which step you missed is what changes the next one.

Practise the rest of the 11

The other 8 questions on this skill are in the free question bank, filterable by difficulty, each with the same worked explanation. No account and no card.

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Frequently asked questions

How many ACT linear equations questions does Prep36 have?
11, each tagged to this skill and each with a worked explanation.
Are these real ACT questions?
No. They are original questions written to the Enhanced ACT format. Prep36 is not affiliated with ACT, Inc.
Is the Math section part of the composite?
Yes. On the Enhanced ACT the composite is the average of English, Math and Reading. Science is optional and reported separately.
Keep readingACT Math practiceEvery Math skill in one place.How many questions can you miss?The miss budget for every score.ACT Score CalculatorTurn raw scores into a composite.
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