How do you find the slope given (c, d) and (c, 1/d)?

Jul 19, 2016

The slope is undefined and the line is a vertical line through $x$ at $c$
Whenever the $x$ value of two points of a line are the same value the slope is undefined.

Explanation:

Slope which is the change in $x$ versus the change in $y$.

Slope is identified by the letter $m$

$m = \frac{\Delta y}{\Delta x}$

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$\left(c , d\right)$ and $\left(c , \frac{1}{d}\right)$

${x}_{1} = c$
${y}_{1} = d$
${x}_{2} = c$
${y}_{2} = \frac{1}{d}$

$m = \frac{\frac{1}{d} - d}{c - c}$

$m = \frac{\frac{1}{d} - \frac{d}{d}}{c - c}$

$m = \frac{\frac{1 - d}{d}}{0}$

Because the numerator is $0$ this fraction is undefined

$m =$ undefined

The slope is undefined and the line is a vertical line through $x$ at $c$
Whenever the $x$ value of two points of a line are the same value the slope is undefined.