What is the slope-intercept form of the line passing through  (-6, 8) and (-3, 5) ?

Dec 7, 2017

$y = - x + 2$

Explanation:

Alright, so this is a two-part question. First we need to find the slope, then we need to find the y-intercept. Finally we plug all this into the slope intercept equation $y = m x + b$

The slope is commonly referred to as $m = \frac{r i s e}{r u n}$ this can also be expressed as $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$ by using the change in $y$ and the change in $x$.

$m = \frac{5 - 8}{- 3 - \left(- 6\right)}$

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

$\textcolor{red}{m = - 1}$

Alright, now lets find the y-intercept by using that slope. If we plug that slope into the base formula we get $y = - x + b$. Since we already know one point, lets put $\left(- 3 , 5\right)$ into that equation and solve for $b$.

$5 = - \left(- 3\right) + b$

$5 - 3 = 3 + b - 3$

$\textcolor{red}{2 = b}$

Now is if plug out $b$ into out equation, we get a finally answer of $\textcolor{red}{y = - x + 2}$

Even though we're done, lets check it by putting in the other point.

$8 = - \left(- 6\right) + 2$

$8 - 6 = 6 + 2 - 6$

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

Hope this helps!
~Chandler Dowd