# How do you write an equation in slope intercept form given (–1, 3) and (1, 7)?

Feb 6, 2017

$y = \textcolor{red}{2} x + \textcolor{b l u e}{5}$

#### Explanation:

Given the two points we can write an equation in point-slope form and then convert it to slope-intercept form. First we must determine 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:

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

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

$m = \frac{4}{2} = 2$

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.

We can now use the slope we calculated and the second point to write an equation in the point-slope form:

$\left(y - \textcolor{red}{7}\right) = \textcolor{b l u e}{2} \left(x - \textcolor{red}{1}\right)$

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 solve our equation for $y$ to transform it to this form.

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

$y - \textcolor{red}{7} = 2 x - 2$

$y - \textcolor{red}{7} + 7 = 2 x - 2 + 7$

$y - 0 = 2 x + 5$

$y = \textcolor{red}{2} x + \textcolor{b l u e}{5}$