Proportional Line Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Proportional Line.
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 straight line that passes through the origin, representing a proportional relationship of the form y = kx with constant ratio k.
When x = 0, y = 0. The line passes through the origin—no head start.
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: Proportional lines have y-intercept zero; all points have the same y/x ratio.
Common stuck point: y = mx + b is linear; only y = mx (b = 0) is proportional.
Sense of Study hint: Check whether the point (0, 0) satisfies the equation. If not, the relationship is not proportional.
Worked Examples
Example 1
easySolution
- 1 Let x = cups of sugar, y = cups of flour.
- 2 The ratio is \frac{y}{x} = \frac{3}{2}, so k = \frac{3}{2}.
- 3 The proportional relationship is y = \frac{3}{2}x.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
mediumBackground Knowledge
These ideas may be useful before you work through the harder examples.