Question

Fill in the blanks below.Find the slope of the line passing through the points (-8, 4) and (-8. - 9).slope: ___

Answer 1

Solution:

The slope of a line that passes through two given points A and B, is expressed as

$\begin{gathered} slope=\frac{y_2-y_1}{x_2-x_1} \\ where \\ (x_1,y_1)\text{ and \lparen x}_2,y_2)\text{ are the coordinates of the points through} \\ which\text{ the line passes.} \end{gathered}$

Given that the line passes through the points (-8, 4) and (-8, -9), this implies that

$\begin{gathered} x_1=-8 \\ y_1=4 \\ x_2=-8 \\ y_2=-9 \end{gathered}$

By substituting these values into the slope formula, we have

$\begin{gathered} slope\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-9-4}{-8-(-8)} \\ =\frac{-9-4}{-8+8} \\ =\frac{-13}{0} \\ \Rightarrow slope=\infty \end{gathered}$

Hence, the slope of the line that passes through the points (-8, 4) and (-8. - 9) is evaluated to be

at infinity.