Answer
Refer to the graph below.
Work Step by Step
Solve for y.
Subtract $2x$ to both sides:
$2x+3y−2x=9−2x
\\3y=9−2x
\\3y=−2x+9$
Divide 3 to both sides:
$\dfrac{3y}{3}=\dfrac{−2x+9}{3}
\\y=−\dfrac{2}{3}x+3$
This means the given equation is equivalent to and has the same graph as $y=−\frac{2}{3}x+3$.
This equation has:
slope = $−\frac{2}{3}$
y-intercept: $(0, 3)$
To graph the given equation, perform the following steps:
(1) Plot the y-intercept $(0, 3)$
(2) Use the slope to plot another point.
From $(0, 3)$, move 2 units down (the rise) and 3 units to the right (the run) to reach $(3, 1)$. Plot $(3, 1)$.
(3) Connect the two points using a line to complete the graph.
(Refer to the attached image in the answer part above for the graph.)