How do you write the equation in slope-intercept form of the line that contains the points (4, -7) and (0, 5),?

Jan 25, 2017

$y = \textcolor{red}{- 3} x + \textcolor{b l u e}{5}$

Explanation:

First, we must find the slope.

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:

$m = \frac{\textcolor{red}{5} - \textcolor{b l u e}{- 7}}{\textcolor{red}{0} - \textcolor{b l u e}{4}}$

$m = \frac{\textcolor{red}{5} + \textcolor{b l u e}{7}}{\textcolor{red}{0} - \textcolor{b l u e}{4}}$

$m = \frac{12}{-} 4$

$m = - 3$

The second point in the problem gives us the y-intercept = $\textcolor{b l u e}{5}$

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.

Substituting the slope and the y-intercept gives:

$y = \textcolor{red}{- 3} x + \textcolor{b l u e}{5}$