Answer
(a) $\frac{x}{a}+\frac{y}{b} = 1$
(b) $4x-3y -24 = 0$
Work Step by Step
(a) Let the equation of a straight line be $~~y = mx+b$
Suppose the x-intercept is $a$.
$y = mx+b$
$0 = m(a)+b$
$ma = -b$
$m = -\frac{b}{a}$
Then:
$y = mx+b$
$y = (-\frac{b}{a})x+b$
$y-b = -\frac{bx}{a}$
$-\frac{y}{b}+1 = \frac{x}{a}$
$\frac{x}{a}+\frac{y}{b} = 1$
(b) $\frac{x}{a}+\frac{y}{b} = 1$
$\frac{x}{6}+\frac{y}{(-8)} = 1$
$4x-3y = 24$
$4x-3y -24 = 0$
