y=mx+c

## y=mx+c

All straight lines can be written as y = mx + c, where the m and c are numbers.

The m gives you the slope, or gradient of the line.

Gradients can be positive or negative. A line rising from left to right is a positive gradient. A line falling from left to right gives a negative gradient.

Up and along can each be negative. Moving bottom to top is positive, and left to right is positive.

The c gives the intercept on the y-axis ie when x = 0.

## Example 1

What is the gradient and intercept of the line y = -4x - 3?

From y = mx + c, m = -4 and c = -3.

## Example 2

Two points on a line are (0, 4) and (1, 7). What is the equation of the line?

It moves along 1 (from 0 to 1).

The line moves up 3 (from 4 to 7).

The gradient is frac(3)(1): m = 3

Write the equation as y = 3x + c

When x = 0, y = 4

4 = 3 xx 0 + c therefore c = 4

y = 3x + 4

Answer: y = 3x + 4