# How do you write the equation in slope intercept form given (-3,0) , (0,9)?

Feb 21, 2017

$y = \textcolor{red}{3} x + \textcolor{b l u e}{9}$

#### Explanation:

First, we need to 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:

$m = \frac{\textcolor{red}{9} - \textcolor{b l u e}{0}}{\textcolor{red}{0} - \textcolor{b l u e}{- 3}} = \frac{\textcolor{red}{9} - \textcolor{b l u e}{0}}{\textcolor{red}{0} + \textcolor{b l u e}{3}} = \frac{9}{3} = 3$

Next, we can use the point-slope formula to write an equation for the line. 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.

Substituting the slope we calculated and the second point gives:

$\left(y - \textcolor{red}{9}\right) = \textcolor{b l u e}{3} \left(x - \textcolor{red}{0}\right)$

$y - \textcolor{red}{9} = 3 x$

Now we can convert this format to the slope intercept form. 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. Solving for $y$ gives:

$y - \textcolor{red}{9} + 9 = 3 x + 9$

$y - 0 = 3 x + 9$

$y = \textcolor{red}{3} x + \textcolor{b l u e}{9}$