Linear Functions Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Linear Functions.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
A function whose graph is a straight line, characterized by a constant rate of change between any two points.
Every step right changes y by the same amount—like climbing stairs at a constant pace.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Linear functions model constant rates and proportional relationships.
Common stuck point: The y-intercept is where the line crosses the y-axis (when x = 0).
Sense of Study hint: Plug in x = 0 to find the y-intercept, then use the slope to find one more point and draw the line.
Worked Examples
Example 1
easySolution
- 1 The slope-intercept form is y = mx + b.
- 2 Substitute m = 2 and b = -3.
- 3 The equation is y = 2x - 3.
Answer
Example 2
mediumExample 3
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
hardBackground Knowledge
These ideas may be useful before you work through the harder examples.