Correct Answer - Option 3 : a = 2, b = 3

__CONCEPT__**:**

If a line cuts the intercepts a and b on the X and Y – axis respectively, then the equation of such line is given as: \(\frac{x}{a} + \frac{y}{b} = 1\)

__CALCULATION__**:**

Given: The straight line \(\frac{x}{a} + \frac{y}{b} = 1\) passes through the points (8, - 9) and (12, - 15)

i.e The points (8, - 9) and (12, - 15) will satisfy the equation \(\frac{x}{a} + \frac{y}{b} = 1\)

\(⇒ \frac{8}{a} - \frac{9}{b} = 1\) -----(1)

\(⇒ \frac{12}{a} - \frac{15}{b} = 1\) -----(2)

From equation (1) and (2), we get

\(⇒ \frac{8}{a} - \frac{9}{b} = \frac{12}{a} - \frac{15}{b}\)

⇒ a = 2b/3 -----(2)

By substituting a = 2b/3 in the equation (1), we get

⇒ \(\frac{24}{2b} - \frac{9}{b} = 1\)

⇒ b = 3

So by substituting b = 3 in (2), we get

⇒ a = 2

Hence, option C is the correct answer