Question

Find the slope of the line that passes through each pair of points.

$\left(6,-3\right),\left(6,4\right)$

Short answer

The slope of the line that passes through the given pair of points isundefined.

Step-by-step solution

Step 1. Write the formula to find the slope of the line that passes through two points.

The slope of the line (m) that passes through the two points $\left(x_1,y_1\right)$and $\left(x_2,y_2\right)$is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Step 2. Find the slope of the line that passes through the points 6,−3 and 6,4.

The slope of the line (m) that passes through the points$\left(x_1,y_1\right)=\left(6,-3\right)$ and$\left(x_2,y_2\right)=\left(6,4\right)$ is:

$$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{4-\left(-3\right)}{6-6} \\ =\frac{4+3}{0} \\ =\frac{7}{0} \\ =\text{undefined} \end{gathered}$$

The slope of the line that passes through the given pair of points isundefined.