How do you graph the equation 3y – 2x = 6 on a coordinate plane?

Apr 9, 2015

Convert the equation $3 y - 2 x = 6$to slope-intercept form.

$3 y = 2 x + 6$

Divide both sides by 3.

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

The slope is $\frac{2}{3}$ and the y-intercept is $2$.

Determine some points on the line by making x=0 and y=0.

If $x = 0$:
$y = \frac{2}{3} \cdot 0 + 2$
$y = 2$
Point = $\left(0 , 2\right)$

If $y = 0$:
$0 = \frac{2}{3} x + 2$
$- \frac{2}{3} x = 2$
Multiply times both sides by 3.
$- 2 x = 6$
Divide both sides by -2.
$x = - 3$
Point=$\left(- 3 , 0\right)$

graph{y=2/3x+2 [-10, 10, -5, 5]}

Apr 9, 2015

$3 y - 2 x = 6$ is a straight line function
so the easiest way to graph it is to establish two points on the line.
In a case like this one the easiest two points to establish are the x and y intercepts.
By inspection
x-intercept occurs at $\left(- 3 , 0\right)$
y-intercept occurs at $\left(0 , 2\right)$

Make these two points on a graph and draw the straight line that runs through both of them. 