# What is the equation of the line between (-7,2) and (7,-38)?

Jun 25, 2018

Slope-intercept form: $y = - \frac{20}{7} x - 18$
Standard form: $20 x + 7 y = - 126$

#### Explanation:

I will assume that you want the equation in slope-intercept form. Here, we can use the format for finding the slope given two points, which is

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

In our problem $\left({x}_{1} , {y}_{1}\right)$ is $\left(- 7 , 2\right)$ and $\left({x}_{2} , {y}_{2}\right)$ $\left(7 , - 38\right)$. We can insert values and find the slope:

$\frac{- 38 - 2}{7 - \left(- 7\right)} = - \frac{40}{7 + 7} = - \frac{40}{14} = - \frac{20}{7}$

Next, we choose one of our coordinates and put that into the formula for a line in slope-intercept form,

$y = m x + b$

Let's choose $\left(- 7 , 2\right)$:

$2 = - \frac{20}{7} \left(- 7\right) + b$
$2 = 20 + b$
$- 18 = b$

This gives us our final equation, $y = - \frac{20}{7} x - 18$.

If you needed standard form, here's how we can do that:

$\frac{20}{7} x + y = - 18$
$7 \cdot \left(\frac{20}{7} x + y\right) = \left(- 18\right) \cdot 7$
$20 x + 7 y = - 126$

Hope this helps!