# Question #3efc2

Apr 19, 2016

Gradient is the slope of a graph at point of interest.
For straight line graph it remains same. For curves, it changes as per location of the point of interest.

#### Explanation:

For a straight line graph, select any two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ on the line.
Calculate, $\text{Gradient} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$
Recall that for an equation of line in the form $y = m x + c$,
$m$ is the gradient or the slope of the line.

Gradient or slope could be positive or negative as shown in the straight line graphs above. Observe the value of $m$.

For curved graphs, one has to draw a tangent at the point of interest. Gradient of the tangent is the gradient of the graph at that point.

This is done by first drawing a line at 90 degrees to the curve at the point where one is required to calculate the gradient of curved graph, a normal or ⊥ line. Then drawing the tangent at 90 degrees to this normal.