Answer
x-intercept = 4
y-intercept = 6
Work Step by Step
RECALL:
(1) The y-intercept can be found by letting $x=0$ and then solving for $y$.
(2) The x-intercept can be found by letting $y=0$ and then solving for $x$.
Solve for the x-intercept by letting $y=0$ and then solving for $x$:
$\frac{1}{2}x+\frac{1}{3}y=2
\\\frac{1}{2}x-\frac{1}{3}(0) = 2
\\\frac{1}{2}x-0=2
\\\frac{1}{2}x=2
\\x=2(2)
\\x=4$
Solve for the y-intercept by letting $x=0$ and then solving for $y$:
$\frac{1}{2}x+\frac{1}{3}y=2 \\
\frac{1}{2}(0)+\frac{1}{3}y=2
\\0+\frac{1}{3}y=2
\\\frac{1}{3}y=2
\\y=2(3)
\\y=6$
Thus, the given equation has:
x-intercept = 4
y-intercept = 6
Plot the intercept points $(0, 6)$ and $(4, 0)$.
Then, connect them using a line to complete the graph.
(refer to the attached image in the answer part above for the graph)
