# What is the slope-intercept form of the line passing through  (-3, -5)  and  (-4, 1) ?

Aug 3, 2016

$y = - 6 x - 23$

#### Explanation:

Slope-intercept form is the common format used for linear equations. It looks like $y = m x + b$, with $m$ being the slope, $x$ being the variable, and $b$ is the $y$-intercept. We need to find the slope and the $y$-intercept to write this equation.

In order to find the slope, we use something called the slope formula. It is $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$. The $x$s and $y$s refer to the variables within coordinate pairs. Using the pairs we are given, we can find the slope of the line. We choose what set is the $2$s and which is the $1$s. It makes no difference which one is which, but I set mine up like this: $\frac{- 5 - 1}{- 3 - - 4}$. This simplifies down to $- \frac{6}{1}$, or just $- 6$. So our slope is $- 6$. Now let's move on to the $y$-intercept.

I'm sure there are other ways to find the $y$-interccept (the value of $y$ when $x = 0$), but I'm going to use the table method.

$\textcolor{w h i t e}{- 4} X \textcolor{w h i t e}{\ldots \ldots} | \textcolor{w h i t e}{\ldots \ldots} \textcolor{w h i t e}{-} Y$
$\textcolor{w h i t e}{.} - 4 \textcolor{w h i t e}{\ldots \ldots} | \textcolor{w h i t e}{\ldots \ldots} \textcolor{w h i t e}{-} 1$
$\textcolor{w h i t e}{.} - 3 \textcolor{w h i t e}{\ldots \ldots} | \textcolor{w h i t e}{\ldots \ldots} \textcolor{w h i t e}{} - 5$
$\textcolor{w h i t e}{.} - 2 \textcolor{w h i t e}{\ldots \ldots} | \textcolor{w h i t e}{\ldots \ldots} \textcolor{w h i t e}{} - 11$
$\textcolor{w h i t e}{.} - 1 \textcolor{w h i t e}{\ldots \ldots} | \textcolor{w h i t e}{\ldots \ldots} \textcolor{w h i t e}{} - 17$
$\textcolor{w h i t e}{. -} 0 \textcolor{w h i t e}{\ldots \ldots} | \textcolor{w h i t e}{\ldots \ldots} \textcolor{w h i t e}{} - 23$

When $x$ is $0$, $y$ is $- 23$. That's our $y$-intercept. And now we have all the pieces we need.

$y = m x + b$
$y = - 6 x - 23$. Just to be safe, let's graph our eqaution and see if we hit the points $\left(- 3 , - 5\right)$ and $\left(- 4 , 1\right)$.
graph{y=-6x-23}
And it does! Great work.