# How do you graph y=3/2x-4 using the slope and intercept?

Oct 16, 2017

See a solution process below:

#### Explanation:

This equation is in 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.

$y = \textcolor{red}{\frac{3}{2}} x - \textcolor{b l u e}{4}$

Therefore:

The $y$-intercept is: $\textcolor{b l u e}{- 4}$ or $\left(0 , \textcolor{b l u e}{- 4}\right)$

The slope is: $\textcolor{red}{m = \frac{3}{2}}$

Slope is rise over rub. So the line will go up $3$ units while it goes to the right $2$ units.

We can plot the $y$-intercept as:

graph{(x^2+(y+4)^2-0.025)=0}

We can plot the next point by going up $3$ units and to the right $2$ units which is at: $\left(2 , - 1\right)$

We can now draw a line through the two points to graph the line:

graph{(x^2+(y+4)^2-0.025)((x-2)^2+(y+1)^2-0.025)(y-(3/2)x+4)=0}