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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. In Coordinate Plane, Functions, and Slope, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.

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.
  4. Connect the calculation back to Graphing Simple Linear Equations so the method, not just the arithmetic, is clear.

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.
  5. Write the final response in the form requested by the prompt.

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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