Answer
See below.
Work Step by Step
The x-intercept is when $y=0$. If this is at $x=a$, then subbing that into the equation: $\frac{a}{a}+\frac{y}{b}=1\\1+\frac{y}{b}=1\\\frac{y}{b}=0\\y=0$
Thus it is indeed the x-intercept.
The y-intercept is when $x=0$. If this is at $y=b$, then subbing that into the equation: $\frac{x}{a}+\frac{b}{b}=1\\\frac{x}{a}+1=1\\\frac{x}{a}=0\\x=0$
Thus it is indeed the y-intercept.
