The ratio of vertical change to horizontal change of a line is defined by point gradient. A gradient is also known as a derivative. The gradient of a line is  m =
$$\begin{array}{l}\frac{rise}{run}\end{array}$$
.

m = point gradient of a line.

The formula is:

$\large m=\frac{y-y_{1}}{x-x_{1}}$

### Solved Example

Question: Find the equation of the straight line that has slope m = 4 and passes through the point (–1, –5).

Solution:

Given,

$$\begin{array}{l}\left( x_{1},y_{1}\right )\end{array}$$
= (–1, –5)

m = 4

$$\begin{array}{l}y – y_1 = m \left( x – x_1 \right )\end{array}$$
$$\begin{array}{l}y – (-5) = 4 \left (x – (-1) \right )\end{array}$$
$$\begin{array}{l}y + 5 = 4 \left ( x+1 \right )\end{array}$$