Question

Find the slope of the line throughP and Q.

$P\left(10,2\right)$and $Q\left(6,-5\right)$

Short answer

The slope of the line through P and Q is $\frac{7}{4}$.

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.

$$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \left(x_1,y_1\right):\left(10,2\right) \\ \left(x_2,y_2\right):\left(6,-5\right) \\ m=\frac{-5-2}{6-10} \end{gathered}$$

Step 3. Calculate the slope.

$\begin{array}{l}m=\frac{-5-2}{-4}\\ m=\frac{-7}{-4}\\ m=\frac{7}{4}\end{array}$

Hence, the slope is $\frac{7}{4}$.