Answer
x-intercept: $(40, 0)$
y-intercept: $(0, -\frac{80}{7})$
Work Step by Step
Find the x-intercept by setting $y=0$ then solving for $x$:
$2x-7y=80
\\2x-7(0)=80
\\2x=80
\\\frac{2x}{2}=\frac{80}{2}
\\x=40$
Thus, the x-intercept is $(40, 0)$.
Find the y-intercept by setting $x=0$ then solving for $y$:
$2x-7y=80
\\2(0)-7y=80
\\-7y=80
\\\frac{-7y}{-7}=\frac{80}{-7}
\\y=-\frac{80}{7}\approx -11.429$
Thus, the y-intercept is $(0, -\frac{80}{7})$.
Use a graphing utility to graph the equation and verify the intercepts.
(Refer to the attached image below for the graph.)
