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Linear Equations and Graphs Checkpoint

A free College Algebra lesson from the “Linear Equations and Inequalities” unit, with a worked example and practice problems including step-by-step solutions.

This checkpoint reviews the linear foundation for College Algebra: equations, inequalities, slope, line forms, and related lines.

What you'll learn

Why it matters: This checkpoint shows whether a student can move between solving, graphing, and interpreting linear relationships. That foundation supports placement readiness because later College Algebra topics still rely on equations, intervals, slope, and line forms.

Worked example

Problem. Find the slope through (1, 4) and (5, 12).

  1. Change in y is 8.
  2. Change in x is 4.
  3. Slope is 8/4 = 2.

Answer: 2

Lesson preview: this page shows 5 practice items. The interactive activity contains 25 practice items and 25 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. Solve 4x - 9 = 23.

Show solution
  1. Add 9, then divide by 4.

Answer: 8

2. Solve -3x < 18. Enter the boundary number.

Show solution
  1. Divide by -3 and reverse the sign.

Answer: -6

3. Find the slope through (2, 7) and (8, 19).

Show solution
  1. 12/6 = 2.

Answer: 2

4. A line with slope 4 through (3, 5) can be written as...

Choices: y - 5 = 4(x - 3) · y - 3 = 4(x - 5) · y + 5 = 4(x + 3) · y = 4x + 5

Show solution
  1. Use point-slope form.

Answer: y - 5 = 4(x - 3)

5. Solve 2(3x - 4) = 22.

Show solution
  1. Divide by 2, add 4, then divide by 3.

Answer: 5

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