A line passes the point (2, -8) and has a slope of -7, how do you write an equation for this line?

Dec 26, 2016

$y + \textcolor{red}{8} = \textcolor{b l u e}{- 7} \left(x - \textcolor{red}{2}\right)$

or

$y = \textcolor{b l u e}{- 7} x + \textcolor{red}{6}$

Explanation:

To find the equation for this line we can use the point-slope formula:

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 $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

In this problem we have been given the slope $\textcolor{b l u e}{m = - 7}$

We have also been given a point on the line $\textcolor{red}{\left(\left(2 , - 8\right)\right)}$

Substituting these into the formula gives:

$\left(y - \textcolor{red}{- 8}\right) = \textcolor{b l u e}{- 7} \left(x - \textcolor{red}{2}\right)$

$y + \textcolor{red}{8} = \textcolor{b l u e}{- 7} \left(x - \textcolor{red}{2}\right)$

If we want to put this into slope-intercept form we can solve for $y$.

The slope-intercept form of a linear equation is:

$y = \textcolor{b l u e}{m} x + \textcolor{red}{b}$

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

$y + \textcolor{red}{8} = \textcolor{b l u e}{- 7} x + \left(\textcolor{b l u e}{- 7} \cdot \textcolor{red}{- 2}\right)$

$y + \textcolor{red}{8} = \textcolor{b l u e}{- 7} x + \textcolor{red}{14}$

$y + \textcolor{red}{8} - \textcolor{g r e e n}{8} = \textcolor{b l u e}{- 7} x + \textcolor{red}{14} - \textcolor{g r e e n}{8}$

$y + 0 = \textcolor{b l u e}{- 7} x + \textcolor{red}{6}$

$y = \textcolor{b l u e}{- 7} x + \textcolor{red}{6}$