# What is the slope of the line passing through the following points:  (5, -6) , (2, 5)?

Mar 8, 2018

$S l o p e = - \frac{11}{3}$

#### Explanation:

$\textcolor{b l u e}{\text{Slope of a line (m)} = \frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}}}$

Here , $\textcolor{red}{{x}_{1} = 5}$

$\textcolor{red}{{y}_{1} = - 6}$

$\textcolor{red}{{x}_{2} = 2}$

$\textcolor{red}{{y}_{2} = 5}$

Put these values in the slope equation

$\implies \textcolor{m a \ge n t a}{S l o p e = \frac{\left(- 6\right) - \left(5\right)}{\left(5\right) - \left(2\right)}}$

$\implies \textcolor{m a \ge n t a}{S l o p e = \frac{- 6 - 5}{5 - 2}}$

$\implies \textcolor{g r e e n}{S l o p e = - \frac{11}{3}}$

Mar 8, 2018

Hey!
Algebra is gr8. In this case, what you would do is use the slope formula; $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$.

#### Explanation:

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

Where m = slope, and each 'y' or 'x' term is inserted from your coordinate points!

(5, -6)(2, 5)

'5' is ${x}_{1}$
'-6' is ${y}_{1}$
'2' is ${x}_{2}$
'5' is ${y}_{2}$
(Respectively, if you haven't noticed :)

Plug them in!

$m = \frac{5 - \left(- 6\right)}{2 - 5}$
(Remember, two negatives cancel out, so the top will be 5 + 6)

$m = \frac{5 + 6}{2 - 5}$
$m = \frac{11}{-} 3$

Your slope is $- \frac{11}{3}$!
Or approximately 3.67 (rounded)