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       $\frac{rise}{run}$

M = point gradient of a line. The formula is:

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

### Solved Examples

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

Solution:

Given,

$\left( x_{1},y_{1}\right )$=(–1, –5)

m=4

Point Gradient Formula: $y – y_1 = m \left( x-x_1 \right )$

$y-(-5) = 4 \left (x-(-1) \right )$
$y + 5 = 4 \left ( x+1 \right )$
y = 4x + 4 – 5
y = 4x – 1