# How do you write an equation in slope-intercept form of the line that passes through the given points (3,5) and (0,4)?

Feb 12, 2017

$y = \textcolor{red}{\frac{1}{3}} x + \textcolor{b l u e}{4}$

#### Explanation:

First, we must determine the slope of the equation. 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:

$m = \frac{\textcolor{red}{4} - \textcolor{b l u e}{5}}{\textcolor{red}{0} - \textcolor{b l u e}{3}} = \frac{- 1}{-} 3 = \frac{1}{3}$

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.

The y-intercept is one of the points given in the problem - (0, 4) or a y-intercept of $\textcolor{b l u e}{4}$

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

$y = \textcolor{red}{\frac{1}{3}} x + \textcolor{b l u e}{4}$