Question

Find the slope of the line through the given points.

$\left(-3,-5\right),\left(-6,7\right)$

Short answer

The slope of the line through the points$\left(-3,-5\right),\left(-6,7\right)$ is$-4$ .

Step-by-step solution

Step 1. Given Information.

The given points are$\left(-3,-5\right),\left(-6,7\right)$

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$\left(x_1,y_1\right)=\left(-3,-5\right)$and$\left(x_2,y_2\right)=\left(-6,7\right)$into the slope formula then simplify it.

$\begin{array}{c}\frac{y_2-y_1}{x_2-x_1}=\frac{7-\left(-5\right)}{-6-\left(-3\right)}\\ \frac{y_2-y_1}{x_2-x_1}=\frac{12}{-3}\\ \frac{y_2-y_1}{x_2-x_1}=-4\end{array}$

Step 4. Conclusion.

The slope of the line through the points$\left(-3,-5\right),\left(-6,7\right)$is$-4$.