# 10.2.1 Gradient of a Straight Line (Sample Questions)

Example 1:
Given that a straight line passes through points (-3, -7) and (4, 14). What is the gradient of the straight line?

Solution:

Let (x1, y1) = (-3, -7) and (x2, y2) = (4, 14).

$\begin{array}{l}=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\\ =\frac{14-\left(-7\right)}{4-\left(-3\right)}\\ =\frac{21}{7}=3\end{array}$

Example 2:

The gradient of the straight line PQ in the diagram above is

Solution:
Let (x1, y1) = (12, 0) and (x2, y2) = (0, 7).

Gradient of the straight line PQ
$\begin{array}{l}=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\\ =\frac{7-0}{0-12}\\ =-\frac{7}{12}\end{array}$

Example 3:
A straight line with gradient -3 passes through points (-4, 6) and (-1, p). Find the value of p.

Solution:
$\begin{array}{l}\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}=-3\\ \frac{p-6}{-1-\left(-4\right)}=-3\\ \frac{p-6}{3}=-3\\ p-6=-9\\ p=-3\end{array}$