# How do you find the slope given (a,3) and (3,a)?

Sep 9, 2016

The slope is $- 1$

#### Explanation:

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

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

Hence, slope of line given $\left(a , 3\right)$ and $\left(3 , a\right)$ is

$\frac{a - 3}{3 - a}$

= (a-3)/(-(a-3)

= $- 1$

Sep 9, 2016

$m = - 1$

#### Explanation:

The formula for slope is $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$m = \frac{3 - a}{a - 3}$

Using a "switch-round" technique by dividing the numerator by a common factor of $- 1$ we get

$m = \frac{- \left(a - 3\right)}{\left(a - 3\right)}$

$m = - 1$