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Graphing Simple Linear Equations

A free Pre-Algebra lesson from the “Coordinate Plane, Functions, and Slope” unit, with a worked example and practice problems including step-by-step solutions.

A linear equation graphs as a straight line. To graph one, choose input values, calculate output values, and plot the ordered pairs. In y = mx + b, b is the y-intercept and m describes the rate of change.

What you'll learn

Why it matters: Phone-plan costs, distance over time on a road trip, and savings growth all graph as straight lines. The slope is the rate; the intercept is the starting amount.

Worked example

Problem. Find three points on y = 2x + 1 using x = 0, 1, and 2.

  1. When x = 0, y = 2(0) + 1 = 1.
  2. When x = 1, y = 2(1) + 1 = 3.
  3. When x = 2, y = 2(2) + 1 = 5.

Answer: (0, 1), (1, 3), (2, 5)

Practice problems

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

Show solution
  1. Warm-up: First identify exactly what the question is asking: For y = 2x, what is y when x = 4?
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Substitute x = 4.
  4. y = 2 x 4 = 8.
  5. Check the result by substituting or estimating: the response should match 8 and make sense in the original problem.

Answer: 8

2. For y = x + 3, what is y when x = 5?

Show solution
  1. Warm-up: First identify exactly what the question is asking: For y = x + 3, what is y when x = 5?
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Substitute x = 5.
  4. y = 5 + 3 = 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 point lies on y = 3x?

Choices: (2, 6) · (2, 5) · (6, 2) · (3, 1)

Show solution
  1. Warm-up: First identify exactly what the question is asking: Which point lies on y = 3x?
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. When x = 2, y = 3 x 2 = 6.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: (2, 6)

4. For y = 4x - 1, what is y when x = 3?

Show solution
  1. Core Practice: First identify exactly what the question is asking: For y = 4x - 1, what is y when x = 3?
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. Substitute x = 3.
  4. 4(3) - 1 = 12 - 1 = 11.
  5. Check the result by substituting or estimating: the response should match 11 and make sense in the original problem.

Answer: 11

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

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

Answer: 5

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