#### Example 1

- The graph of the line with equation y = 2x + 1.

The y-intercept is 1 and the gradient = \(\dfrac{2}{1} = 2\).

Detailed description - The graph of the line with equation \(y=−2x+1.\)

The y-intercept is 1 and the gradient \(y=\dfrac{−2}{1}=−2.\)

Detailed description

#### In summary

Equations of the form y = mx + c

The graph of each equation is a straight line, m is the **gradient** of the line and c is the y-**intercept**.
Conversely, if a straight line has gradient m and y-intercept c it has equation y = mx + c.

#### Example 2

Write down the gradient and y-intercept of the lines and state which way each slopes:

- y = 9x + 2
- y = −x + 8

#### Solution

- The gradient is 9. The y-intercept is 2. The gradient is positive so the line slopes up from left to right.
- The gradient is −1. The y-intercept is 8. The gradient is negative so the line slopes down from left to right.