# How do you write an equation of the line with an x-intercept of 2, and y-intercept of -3?

Feb 15, 2016

The equation is $y = \frac{3}{2} x - 3$

#### Explanation:

I found the equation by using the $y = m x + b$ formula, where $m$ is the slope and $b$ is the $y$-intercept. In this case we are given the $y$-intercept, which is $- 3$, or $\left(0 , - 3\right)$.

So now we have $b$, and we still need to find $m$, or the slope. Now how are we going to find that? Well, the slope is rise over run, so we could graph two points and count the points it goes up and the points it goes over and write it as a ratio. If we want to do that, first things first, we'd need two points. And I think we have them! The $y$-intercept was $\left(0 , - 3\right)$. The $x$-intercept was $2$, which can be rewritten into a coordinate pair to read $\left(2 , 0\right)$!

Now we have two points. We could graph the two and find the slope by counting, or we could use another formula, which looks like this: $\frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{g r e e n}{{x}_{2}} - \textcolor{p u r p \le}{{x}_{1}}}$. Let's assign a name for our coordinate pairs. $\left(0 , - 3\right)$ can be $\left(\textcolor{g r e e n}{{x}_{2}} , \textcolor{red}{{y}_{2}}\right)$, and $\left(2 , 0\right)$ can be $\left(\textcolor{p u r p \le}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right)$. Now we have $\frac{\textcolor{red}{- 3} - \textcolor{b l u e}{0}}{\textcolor{g r e e n}{0} - \textcolor{p u r p \le}{2}}$, which can be simplified to $\frac{- 3}{-} 2$ or just $\frac{3}{2}$. NOW we have $m$, and we can write our equation.

$y = m x t b$ becomes $y = \frac{3}{2} x - 3$. And to double check, let's graph our equation and make sure that the $x$-intercept is at $2$ and that the $y$-intercept is at -3.
graph{y=3/2x-3}

Which it is! Good job, we got it right!