Linear Relationships Practice Questions

Common Core (US) · Common Core Algebra 1 · 131 free MCQs with instant results and detailed explanations.

131

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Sample Questions from Linear Relationships

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Easy

If a line passes through the points (2, 3) and (4, 7), what is its slope?

A. 2

B. 1

C. 3

D. 4

Show Answer & Explanation

Correct Answer: A

The slope (m) is calculated as (y2 - y1) / (x2 - x1). Here, (7 - 3) / (4 - 2) = 4/2 = 2.

Easy

What is the slope of the line represented by the equation y = 2x + 5?

A. 2

B. 5

C. -2

D. 0

Show Answer & Explanation

Correct Answer: A

In the slope-intercept form of a linear equation, y = mx + b, 'm' represents the slope. Here, m = 2.

Easy

If a line passes through the points (1, 2) and (3, 6), what is the slope of the line?

A. 2

B. 3

C. 1

D. 4

Show Answer & Explanation

Correct Answer: A

The slope can be calculated using the formula (y2 - y1) / (x2 - x1). Here, (6 - 2) / (3 - 1) = 4 / 2 = 2.

Medium

A line passes through the points (2, 3) and (4, 7). What is the y-intercept of this line?

A. 1

B. 3

C. 5

D. 0

Show Answer & Explanation

Correct Answer: C

First, find the slope (m) using (y2 - y1)/(x2 - x1). Then, use the point-slope form to find the y-intercept.

Medium

Which of the following equations represents a line that is parallel to y = -2x + 4?

A. y = -2x + 1

B. y = 2x - 4

C. y = -3x + 4

D. y = x + 2

Show Answer & Explanation

Correct Answer: A

Parallel lines have the same slope. The slope of the given line is -2, so the parallel line must also have a slope of -2.

Medium

If a linear function is defined as f(x) = 4x - 1, what is the output f(3)?

A. 11

B. 12

C. 10

D. 7

Show Answer & Explanation

Correct Answer: A

To find f(3), substitute x=3 into the function: f(3) = 4(3) - 1 = 12 - 1 = 11.

Medium

A linear relationship is modeled by the equation y = 5x - 10. What is the value of y when x is increased by 2?

A. 0

B. 5

C. 10

D. 15

Show Answer & Explanation

Correct Answer: B

If x is increased by 2 (from x to x+2), the new equation becomes y = 5(x + 2) - 10, which simplifies to y = 5x + 10 - 10 = 5x + 0.

Hard

A linear equation is represented as 3x - 4y = 12. Which of the following is the y-intercept of this line?

A. -3

B. 3

C. 4

D. -4

Show Answer & Explanation

Correct Answer: A

To find the y-intercept, set x = 0. The equation becomes 3(0) - 4y = 12, which simplifies to -4y = 12. Solving for y gives y = -3, making the y-intercept -3.

Hard

A line in a coordinate plane passes through the points (2, 3) and (4, 7). What is the slope of this line?

A. 2

B. 1.5

C. 0.5

D. 4

Show Answer & Explanation

Correct Answer: A

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1). Substituting the points (2, 3) and (4, 7) gives m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Q10

Hard

A linear equation is modeled as y = 3x - 5. If the output (y) is increased by 9, what is the corresponding change in x?

A. 3

B. 1

C. 2

D. 4

Show Answer & Explanation

Correct Answer: C

To find the change in x when y increases by 9, we start with y = 3x - 5. If y increases by 9, the new equation becomes y + 9 = 3x - 5. Solving for x gives x = (y + 14)/3. The change in x can be calculated as (y + 9 + 5)/3 - (y - 5)/3 = 2.

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More Common Core Algebra 1 Chapters

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Linear Relationships — Common Core (US) Common Core Algebra 1 Practice Questions Online

This page contains 131 practice MCQs for the chapter Linear Relationships in Common Core (US) Common Core Algebra 1. The questions are organized by difficulty — 30 easy, 69 medium, 32 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.