A gradient is the rate of change of one variable compared to another variable.

If there is a change in y

${\displaystyle \delta y=y-y_{1}}$

and there is a change in x

${\displaystyle \delta x=x-x_{1}}$

${\displaystyle m={\frac {\delta y}{\delta x}}={\frac {y-y_{1}}{x-x_{1}}}}$
${\displaystyle \delta y=m\delta x=m(x-x_{1})}$

## Example

two points on a straight line (2,3), (3,4) then the gradient of the straight line is

${\displaystyle m={\frac {4-3}{3-2}}}$