If three points $(h, 0), (a, b),$ and $(0, k)$ lie on a line,show that $\frac{a}{h} + \frac{b}{k} = 1$.

(N/A) If the points $A(h, 0), B(a, b),$ and $C(0, k)$ lie on a line,then the slope of $AB$ must be equal to the slope of $BC$.
Slope of $AB = \frac{b - 0}{a - h} = \frac{b}{a - h}$
Slope of $BC = \frac{k - b}{0 - a} = \frac{k - b}{-a}$
Equating the slopes: $\frac{b}{a - h} = \frac{k - b}{-a}$
Cross-multiplying: $-ab = (k - b)(a - h)$
Expanding the right side: $-ab = ka - kh - ab + bh$
Simplifying: $ka + bh = kh$
Dividing both sides by $kh$: $\frac{ka}{kh} + \frac{bh}{kh} = \frac{kh}{kh}$
Result: $\frac{a}{h} + \frac{b}{k} = 1$.