Prove that

Solution:

To Find: The values of a and b when the line $\frac{x}{a}+\frac{y}{b}=1$ passes through the points (8, -9) and (12, -15).

Given : the equation of the line $: \frac{x}{a}+\frac{y}{b}=1$ equation 1

Also (8, -9) passes through equation 1

$\frac{8}{a}-\frac{9}{b}=1$

8b - 9a = ab equation 2

And (12, -15) passes through equation 1

$\frac{12}{a}-\frac{15}{b}=1$

12b - 15a = ab equation 3

Solving equation 2 and 3

a= 2.

Put a=2 in equation 2

$8 b-9 a=a b$

$8 b-18=2 b$

$6 b=18 \Rightarrow b=3$

Hence the values of a and b are 2 and 3 respectively.