Answer
(a) See prove below.
(b) $4x-3y-24=0$
Work Step by Step
(a) Given the x-intercept as $a$ and the y-intercept as $b$, we have two points on the line as
$(a,0)$ and $(0,b)$, the slope of the line is then given by $m=\frac{b-0}{0-a}=-\frac{b}{a}$.
Thus, the equation of the line can then be written as $y=-\frac{b}{a}x+b$ which gives
$\frac{b}{a}x+y=b$, divide $b$ on both sides, we get $\frac{x}{a}+\frac{y}{b}=1$ which proves the formula.
(b) Given $a=6,b=-8$, the equation becomes $\frac{x}{6}-\frac{y}{8}=1$, multiply 24 on both sides and
rearrange the equation to get $4x-3y-24=0$
