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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)

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

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

Show solution
  1. Substitute x = 4.
  2. y = 2 x 4 = 8.

Answer: 8

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

Show solution
  1. Substitute x = 5.
  2. y = 5 + 3 = 8.

Answer: 8

3. Which point lies on y = 3x?

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

Show solution
  1. When x = 2, y = 3 x 2 = 6.

Answer: (2, 6)

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

Show solution
  1. Substitute x = 3.
  2. 4(3) - 1 = 12 - 1 = 11.

Answer: 11

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

Show solution
  1. In y = mx + b, b is the y-intercept.
  2. Here b = 5.

Answer: 5

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