# How do you write an equation of a line passing through (0,2) and (-5,0)?

May 12, 2017

See a solution process below:

#### Explanation:

First, we need to determine the slope of the line going through these two points. 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:

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

We can now use the slope-intercept formula to write the equation for the line. 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 calculated the slope above. The y-intercept is $\left(0 , 2\right)$. Substituting into the formula gives:

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