# What is the slope of the line passing through the following points: (-7,11), (9, -10) ?

Mar 17, 2018

$\text{slope } = - \frac{21}{16}$

#### Explanation:

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

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(-7,11)" and } \left({x}_{2} , {y}_{2}\right) = \left(9 , - 10\right)$

$\Rightarrow m = \frac{- 10 - 11}{9 - \left(- 7\right)} = \frac{- 21}{16} = - \frac{21}{16}$

Mar 17, 2018

$y = - \frac{21}{16} x + \frac{29}{16}$

#### Explanation:

First we find $m$ which is slope. Slope formula is
$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

Where
${y}_{2} = - 10$
${y}_{1} = 11$
${x}_{2} = 9$
${x}_{1} = - 7$

Now we just plug it in, giving us
$m = \frac{- 10 - 11}{9 - \left(- 7\right)}$

$m = \frac{- 21}{9 + 7}$

$m = \frac{- 21}{16}$

Now that we have $m$ we can use the line formula to finish the problem.
The line formula is
$y - {y}_{1} = m \left(x - {x}_{1}\right)$

$y - 11 = \left(- \frac{21}{16}\right) \left(x - \left(- 7\right)\right)$

$y - 11 = - \frac{21}{16} \left(x + 7\right)$

$y - 11 = - \frac{21}{16} x + \frac{- 21 \left(7\right)}{16}$

$y - 11 = - \frac{21}{16} x - \frac{147}{16}$

Now we add $11$ to both sides giving us
$y = - \frac{21}{16} x - \frac{147}{16} + 11$

Now we find a common denominator between the constants $\frac{11}{1}$ and $- \frac{147}{16}$

$y = - \frac{21}{16} x + \frac{11 \left(16\right)}{1 \left(16\right)} - \frac{147}{16}$

$y = - \frac{21}{16} x + \frac{176}{16} - \frac{147}{16}$

$y = - \frac{21}{16} x + \frac{176 - 147}{16}$

$y = - \frac{21}{16} x + \frac{29}{16}$