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Slope-Intercept Form

A free Algebra I lesson from the “Functions, Linear Relationships, and Rate of Change” unit, with a worked example and practice problems including step-by-step solutions.

Slope-intercept form writes a line as y = mx + b. The number m is the slope, or rate of change, and b is the y-intercept, where the graph crosses the y-axis. This form is useful because it lets you graph quickly: start at the intercept, then use the slope to move from point to point. When practicing, identify m and b before calculating. If the equation is not already solved for y, isolate y first. A common mistake is reading the constant term as the slope or forgetting that a negative slope moves down as x increases.

What you'll learn

Why it matters: Phone plans, delivery fees, savings goals, and subscription costs often have a starting amount plus a steady rate.

Worked example

Problem. Write the equation of a line with slope 2 and y-intercept -3.

  1. Start with y = mx + b.
  2. Replace m with 2 and b with -3.
  3. The equation is y = 2x - 3.

Answer: y = 2x - 3

Practice problems

1. In y = -3x + 4, what is the slope?

Choices: -3 · 3 · 4 · -4

Show solution
  1. Warm-up: First identify exactly what the question is asking: In y = -3x + 4, what is the slope?
  2. For slope or rate of change, compare vertical change to horizontal change and keep the sign attached to the direction of the change.
  3. In y = mx + b, m is the slope.
  4. Here m = -3.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: -3

2. In y = 5x - 8, what is the y-intercept?

Show solution
  1. Warm-up: First identify exactly what the question is asking: In y = 5x - 8, what is the y-intercept?
  2. For intercepts, remember that an x-intercept has y = 0 and a y-intercept has x = 0.
  3. The y-intercept is b.
  4. Here b = -8.
  5. Check the result by substituting or estimating: the response should match -8 and make sense in the original problem.

Answer: -8

3. Which equation has slope 1/2?

Choices: y = 2x + 1 · y = x/2 - 7 · y = -2x · y = 7

Show solution
  1. Warm-up: First identify exactly what the question is asking: Which equation has slope 1/2?
  2. For slope or rate of change, compare vertical change to horizontal change and keep the sign attached to the direction of the change.
  3. x/2 means (1/2)x.
  4. That equation has slope 1/2.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: y = x/2 - 7

4. For y = 4x + 6, what is y when x = 2?

Show solution
  1. Core Practice: First identify exactly what the question is asking: For y = 4x + 6, what is y when x = 2?
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Substitute x = 2.
  4. 4(2) + 6 = 14.
  5. Check the result by substituting or estimating: the response should match 14 and make sense in the original problem.

Answer: 14

5. What is the y-intercept of y = -2x + 9?

Show solution
  1. Core Practice: First identify exactly what the question is asking: What is the y-intercept of y = -2x + 9?
  2. For intercepts, remember that an x-intercept has y = 0 and a y-intercept has x = 0.
  3. The y-intercept is the constant term.
  4. Here b = 9.
  5. Check the result by substituting or estimating: the response should match 9 and make sense in the original problem.

Answer: 9

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