# How do you write the slope-intercept equation of a line containing the points (-7 , 2) and (3, -3)?

Apr 10, 2017

See the entire solution process below:

#### Explanation:

First, we need to find the slope of the equation. The slope can be found by using the formula: $m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $m$ is the slope and ($\textcolor{b l u e}{{x}_{1} , {y}_{1}}$) and ($\textcolor{red}{{x}_{2} , {y}_{2}}$) are the two points on the line.

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{red}{- 3} - \textcolor{b l u e}{2}}{\textcolor{red}{3} - \textcolor{b l u e}{- 7}} = \frac{\textcolor{red}{- 3} - \textcolor{b l u e}{2}}{\textcolor{red}{3} + \textcolor{b l u e}{7}} = - \frac{5}{10} = - \frac{1}{2}$

The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

We know $m = - \frac{1}{2}$ and can substitute this into the equation giving:

$y = \textcolor{red}{- \frac{1}{2}} x + \textcolor{b l u e}{b}$

We can also substitute the values from the first point in the problem and solve for $b$:

$2 = \left(\textcolor{red}{- \frac{1}{2}} \times - 7\right) + \textcolor{b l u e}{b}$

$2 = \frac{7}{2} + \textcolor{b l u e}{b}$

$\textcolor{red}{- \frac{7}{2}} + 2 = \textcolor{red}{- \frac{7}{2}} + \frac{7}{2} + \textcolor{b l u e}{b}$

$\textcolor{red}{- \frac{7}{2}} + \left(\frac{2}{2} \times 2\right) = 0 + \textcolor{b l u e}{b}$

$\textcolor{red}{- \frac{7}{2}} + \frac{4}{2} = \textcolor{b l u e}{b}$

$- \frac{3}{2} = \textcolor{b l u e}{b}$

We can now substitute this along with the slope into the slope-intercept form to give:

$y = \textcolor{red}{- \frac{1}{2}} x + \textcolor{b l u e}{- \frac{3}{2}}$

$y = \textcolor{red}{- \frac{1}{2}} x - \textcolor{b l u e}{\frac{3}{2}}$