Question:
If the straight line $\frac{x}{a}+\frac{y}{b}=1$ passes through the points $(8,-9)$ and $(12,-15)$
find the values of a and b.
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.