# How do you write an equation of a line given (-8,8) and (0,1)?

Jul 28, 2017

See a solution process below:

#### Explanation:

First, we need to determine the slope of the line. 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:

$m = \frac{\textcolor{red}{1} - \textcolor{b l u e}{8}}{\textcolor{red}{0} - \textcolor{b l u e}{- 8}} = \frac{\textcolor{red}{1} - \textcolor{b l u e}{8}}{\textcolor{red}{0} + \textcolor{b l u e}{8}} = - \frac{7}{8}$

We can now use the point-slope formula to write and equation for the line running between the two points in the problem. The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\left(\textcolor{red}{{x}_{1} , {y}_{1}}\right)$ is a point the line passes through.

Substituting the slope we calculated and the values from the first point in the problem gives:

$\left(y - \textcolor{red}{8}\right) = \textcolor{b l u e}{- \frac{7}{8}} \left(x - \textcolor{red}{- 8}\right)$

$\left(y - \textcolor{red}{8}\right) = \textcolor{b l u e}{- \frac{7}{8}} \left(x + \textcolor{red}{8}\right)$

We can also substitute the slope we calculated and the values from the second point in the problem giving:

$\left(y - \textcolor{red}{1}\right) = \textcolor{b l u e}{- \frac{7}{8}} \left(x - \textcolor{red}{0}\right)$

$\left(y - \textcolor{red}{1}\right) = \textcolor{b l u e}{- \frac{7}{8}} x$

We can also solve this equation for $y$ to put it into slope-intercept form. 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.

$y - \textcolor{red}{1} = - \frac{7}{8} x$

$y - \textcolor{red}{1} + 1 = - \frac{7}{8} x + 1$

$y - 0 = - \frac{7}{8} x + 1$

$y = \textcolor{red}{- \frac{7}{8}} x + \textcolor{b l u e}{1}$