# How do you write a equation in slope intercept form of the line passing through the given points (0,2), (1,7)?

Mar 2, 2017

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

#### Explanation:

First, we must find 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:

$m = \frac{\textcolor{red}{7} - \textcolor{b l u e}{2}}{\textcolor{red}{1} - \textcolor{b l u e}{0}} = \frac{5}{1} = 5$

The point $\left(0 , 2\right)$ is the y-intercept.

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 we calculated and the y-intercept gives us:

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