__5.2 Finding the Gradient of a Straight Line__The

**gradient**,*, of a straight line which passes through***m***P*(*x*_{1},*y*_{1}) and*Q*(*x*_{2},*y*_{2}) is given by,

*m*= $\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$

_{PQ}**Example 1:**

Find the gradient of the straight line joining two points

*P*and

*Q*in the above diagram.

*Solution:**P*= (

*x*

_{1},

*y*

_{1}) = (4, 3),

*Q*= (

*x*

_{2},

*y*

_{2}) = (10, 5)

Gradient of the straight line

*PQ*

**Example 2:**

Calculate the gradient of a straight line which passes through point

*A*(7, -3) and point*B*(-3, 6).

Solution:Solution:

*A*= (x

_{1}, y

_{1}) = (7, -3),

*B*= (x

_{2}, y

_{2}) = (-3, 6)

Gradient of the straight line

$$\begin{array}{l}=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\\ =\frac{6-\left(-3\right)}{-3-7}\\ =-\frac{9}{10}\end{array}$$
*AB*