# How do you write the equation in slope intercept form given (2,7) and (-4,1)?

Apr 22, 2017

See the entire solution process below:

#### Explanation:

First, 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:

$m = \frac{\textcolor{red}{1} - \textcolor{b l u e}{7}}{\textcolor{red}{- 4} - \textcolor{b l u e}{2}} = \frac{- 6}{-} 6 = 1$

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 can substitute the slope we calculated and one of the points from the problem for $x$ and $y$ and then solve for $b$:

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

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

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

$5 = 0 + \textcolor{b l u e}{b}$

$5 = \textcolor{b l u e}{b}$

We can now substitute the slope and y-intercept we calculated into the formula:

$y = \textcolor{red}{1} x + \textcolor{b l u e}{5}$