# What is the slope of the line passing through the following points:  (1,3) ; (1,-2)?

Mar 11, 2018

$\text{slope is undefined}$

#### Explanation:

$\text{calculate the slope m using the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(1,3)" and } \left({x}_{2} , {y}_{2}\right) = \left(1 , - 2\right)$

$\rightarrow m = \frac{- 2 - 3}{1 - 1} = - \frac{5}{0}$

$\text{since division by zero is undefined then slope is undefined}$

Mar 11, 2018

Slope=undefined; vertical line

#### Explanation:

The slope is the change in the y-coordinates over the change in x-coordinates. The formula $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$ where m is the slope, shows the change from coordinates ${y}_{1}$ to ${y}_{2}$ and likewise for the x-coordinates. The order that you choose to input the coordinates doesn't matter as long as the corresponding coordinates don't get mixed up. We'll call $\left(1 , 3\right)$ $\left({x}_{1} , {y}_{1}\right)$ and $\left(1 , - 2\right)$ $\left({x}_{2} , {y}_{2}\right)$.

$m = \frac{- 2 - 3}{1 - 1}$
$m = \frac{- 5}{0}$

The formula gives an undefined slope meaning that the line crossing the two points is vertical.