# How do you find the slope given (11, -2) and (2, -2)?

Apr 19, 2018

See below..

#### Explanation:

Slope of a line $m$ passing through $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is given by

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

Plugging in the given values we get

$\text{ } m = \frac{11 - 2}{- 2 + 2}$

which is undefined, and this gives rise to a special case. The line with undefined slope is a line parallel to the $y$-axis.

Also, slope is $\tan \theta$. When $\tan \theta =$undefined, then $\theta = \frac{\pi}{2}$, which is parallel to $y$-axis.

Apr 19, 2018

Nothing, undefined, or $0$

#### Explanation:

We can find the slope or gradient using:

$\frac{\Delta y}{\Delta x}$ Where $\Delta$ means the 'change in...'

Remembering the coordinates are $\left(x , y\right)$

$11 \to 2$ we have to $- 9$

$- 2 \to - 2$ we do nothing.

Therefore using $\frac{\Delta y}{\Delta x}$ -> $\frac{0}{-} 9$-> which is nothing, or undefined.

As dividing by $0$, or multiplying by $0$ gives nothing.