Question

Find the slope of the line through the given points.

$\left(4,2\right),\left(3,8\right)$

Short answer

The slope of the line through the points $\left(4,2\right),\left(3,8\right)$ is$-6$ .

Step-by-step solution

Step 1. Given Information.

The given points are$\left(4,2\right),\left(3,8\right)$.

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 $\left(x_1,y_1\right)=\left(4,2\right)$ and $\left(x_2,y_2\right)=\left(3,8\right)$ into the slope formula then simplify it.

$\begin{array}{c}\frac{y_2-y_1}{x_2-x_1}=\frac{8-2}{3-4}\\ \frac{y_2-y_1}{x_2-x_1}=\frac{6}{-1}\\ \frac{y_2-y_1}{x_2-x_1}=-6\end{array}$

Step 4. Conclusion.

The slope of the line through the points $\left(4,2\right),\left(3,8\right)$ is $-6$.