Answer
Refer to the graph below.
Work Step by Step
Solve for $y$ by dividing both sides of the equation by $3$:
$\frac{3y}{3}=\frac{2x+9}{3}
\\y=\frac{2}{3}x+3$
This means that the equation $3y=2x+9$ is equivalent to, and has the same graph as $y=\frac{2}{3}x+3$.
The equation $y=\frac{2}{3}x+3$ has:
slope = $\frac{2}{3}$
y-intercept: $(0, 3)$
To graph this equation, perform the following steps:
(1) Plot the y-intercept $(0, 3)$.
(2) Use the slope to plot a second point.
From $(0, 3)$, move 2 units up (the rise) and 3 units to the right (the run) to reach the point $(3, 5)$. Plot $(3, 5)$.
(3) Connect the two points using a line to complete the graph.
(Refer to the graph in the answer part above.)
