Question

Find the slope of the line through P and Q.

$P\left(2,-2\right)$and $Q\left(7,-1\right)$

Short answer

Slope of the line through and is $\frac{1}{5}$.

Step-by-step solution

Step 1. Apply the slope formula.

The slope of the line is $m=\frac{y_2-y_1}{x_2-x_1}$,Where $\left(x_1,y_1\right),\left(x_2,y_2\right)$are coordinates of points lie on the line.

Step 2. Substitute the values in the slope formula.

$$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \left(x_1,y_1\right):\left(2,-2\right) \\ \left(x_2,y_2\right):\left(7,-1\right) \\ m=\frac{-1-\left(-2\right)}{7-2} \end{gathered}$$

Step 3. Calculate the slope.

$\begin{array}{l}m=\frac{-1+2}{5}\\ m=\frac{1}{5}\end{array}$

Hence, the slope is $\frac{1}{5}$.