Answer
x-intercept: $(\frac{50}{3}, 0)$
y-intercept: $(0, 25)$
Work Step by Step
Find the x-intercept by setting $y=0$ then solving for $x$:
$3x+2y=50
\\3x+2(0)=50
\\3x=50
\\\frac{3x}{3}=\frac{50}{3}
\\x=\frac{50}{3}\approx 16.67$
Thus, the x-intercept is $(\frac{50}{3}, 0)$.
Find the y-intercept by setting $x=0$ then solving for $y$:
$3x+2y=50
\\3(0)+2y=50
\\2y=50
\\\frac{2y}{2}=\frac{50}{2}
\\y=25$
Thus, the y-intercept is $(0, 25)$.
Use a graphing utility to graph the equation and verify the intercepts.
(Refer to the attached image below for the graph.)
