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Linear Functions Introduction

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 function pairs each input with exactly one output. A linear function has a constant rate of change — its graph is a straight line and its equation looks like y = mx + b (or f(x) = mx + b). Function notation f(x) lets you name the rule and ask for its value at any input. 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: Cell-phone plans with a flat fee plus a per-minute charge, taxi fares (drop fee plus per-mile rate), and any constant-rate scenario produce linear functions.

Worked example

Problem. If f(x) = 3x + 2, find f(4).

  1. Substitute 4 for x: f(4) = 3(4) + 2.
  2. = 12 + 2 = 14.
  3. Connect the calculation back to Linear Functions Introduction so the method, not just the arithmetic, is clear.
  4. Check the result against the original question before writing the final answer.

Answer: 14

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

Practice problems

1. Is y = 2x + 5 a linear function?

Choices: Yes · No

Show solution
  1. Form y = mx + b with m=2 and b=5.
  2. That's a linear function.

Answer: Yes

2. Is y = x^2 a linear function?

Choices: Yes · No

Show solution
  1. x^2 is degree 2 (a parabola).
  2. Linear functions are degree 1.

Answer: No

3. If f(x) = x + 7, find f(3).

Show solution
  1. f(3) = 3 + 7 = 10.

Answer: 10

4. If f(x) = 2x, find f(-3).

Show solution
  1. f(-3) = 2 * (-3) = -6.

Answer: -6

5. A table has (1,3), (2,5), (3,7), (4,9). Linear?

Choices: Yes · No

Show solution
  1. Outputs increase by 2 each step.
  2. Constant difference means linear.

Answer: Yes

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