Question

Find the slope of the line through the given points.

$\left(3,-6\right),\left(-2,2\right)$

Short answer

The slope of the line through the points$\left(3,-6\right),\left(-2,2\right)$is$-\frac{8}{5}$.

Step-by-step solution

Step 1. Given Information.

The given points are$\left(3,-6\right),\left(-2,2\right)$

Step 2. Formula used.

The slope of the line through the points$\left(x_1,y_1\right),\left(x_2,y_2\right)$ is$\frac{y_2-y_1}{x_2-x_1}$ .

Step 3. Calculation.

To find the slope substitute$\left(x_1,y_1\right)=\left(3,-6\right)$and$\left(x_2,y_2\right)=\left(-2,2\right)$into the slope formula then simplify it.

$\begin{array}{c}\frac{y_2-y_1}{x_2-x_1}=\frac{2-\left(-6\right)}{-2-3}\\ \frac{y_2-y_1}{x_2-x_1}=\frac{8}{-5}\end{array}$

Step 4. Conclusion.

The slope of the line through the points $\left(3,-6\right),\left(-2,2\right)$is$-\frac{8}{5}$ .