# y = mx + c

The equation of a straight line. The number m is the gradient and c is where the line crosses the y-axis.

Maths (school) · Part 04: Graphs · Card 3 of 8 · Last updated 2026-10-19

## Analogy

Like a taxi fare: c is the fee when you get in, m is the price per mile.

## Example

**y = 2x + 3**

Gradient m = 2
y-intercept c = 3
When x = 4: y = 2 x 4 + 3 = 11

## In practice

A phone plan costing 10 pounds a month plus 0.50 per gigabyte follows y = 0.5x + 10.

## Practice

### Flashcards

- **In y = mx + c, what do m and c mean?** m is the gradient and c is where the line crosses the y-axis.

### Interview questions

**Find the equation of the straight line through (0, 3) and (2, 7).**

- Gradient = (7 - 3) / (2 - 0) = 2
- The line crosses the y-axis at 3
- So y = 2x + 3
- Check that (2, 7) fits: 2 x 2 + 3 = 7

## Questions people ask

### What is the y-intercept?

The y-intercept is the point where a line crosses the y-axis. On that axis x is zero, so the intercept is the value of y when x = 0. In y = 2x + 3 it is 3, so the line passes through the point (0, 3).

### How do you find the equation of a line from a graph?

Read the y-intercept for c. Then pick two clear points to work out the gradient m by dividing the rise by the run. Put both into y = mx + c. A line crossing at 3 and going up 2 per step is y = 2x + 3.

## Related concepts

- [Gradient](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-2)
- [Parallel and perpendicular lines](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-4)
- [Midpoint of a line](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-5)
- [Coordinates](https://studyvisually.com/learn/science/maths-school/maths-school-part-4/maths-school-part-4-concept-1)

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