Answer
The $x−$ intercept is $3$.
The $y−$ intercept is $-2$.
The slope of the line is $m=\frac{2}{3}$.
The graph is shown below.
Work Step by Step
The given linear equation is
$\Rightarrow 2x-3y=6$
$x-$ intercept.
Substitute $0$ for $y$.
$\Rightarrow 2x-3(0)=6$
Simplify.
$\Rightarrow 2x+0=6$
$\Rightarrow 2x=6$
Divide each side by $2$.
$\Rightarrow \frac{2x}{2}=\frac{6}{2}$
Simplify.
$\Rightarrow x=3$
The $x−$ intercept is $3$, so plot the point $A=(3,0)$
$y-$ intercept.
Substitute $0$ for $x$.
$\Rightarrow 2(0)-3y=6$
Simplify.
$\Rightarrow 0-3y=6$
$\Rightarrow -3y=6$
Divide each side by $-3$.
$\Rightarrow \frac{-3y}{-3}=\frac{6}{-3}$
Simplify.
$\Rightarrow y=-2$
The $y−$ intercept is $-2$, so plot the point $B=(0,-2)$.
Draw a line through the points A and B.
Isolate $y$ of the given equation.
$\Rightarrow y=\frac{2}{3}x-2$
The slope intercept form is $y=mx+c$.
The slope of the line is $m=\frac{2}{3}$.
