# How do you graph the equation by plotting points 3x - 2y =4?

May 7, 2016

Function: $y = - 2 + \frac{3}{2} x$
Intercepts: ($0 , - 2$) and ($\frac{4}{3} , 0$). The graph is a line that passes through these points.

#### Explanation:

First of all, you must make a function out of this equation. A function is defined as $y = f \left(x\right)$, so you can start by isolating $y$:

$- 2 y = 4 - 3 x$
$y = \frac{4 - 3 x}{-} 2 = - 2 + \frac{3}{2} x$

Next, since this is a linear function, you can find the intercepts of the function.
With $x = 0$:
$y = - 2 + \cancel{\frac{3}{2} \cdot \left(0\right)} = - 2$

And with $y = 0$:
$0 = - 2 + \frac{3}{2} x$
$3 \frac{x}{2} = 2$
$3 x = 4$
$x = \frac{4}{3}$

We now have the points ($0 , - 2$) and ($\frac{4}{3} , 0$). We can just make a line that passes through them in the graph:

graph{3/2x-2 [-5, 5, -5, 5]}