Question:
A line cuts off on the coordinate axes positive intercepts whose sum is 4. If it passes through \((9/2,-5)\), its equation is
A line cuts off on the coordinate axes positive intercepts whose sum is 4. If it passes through \((9/2,-5)\), its equation is
Show Hint
Use intercept form when intercept sum is given.
Updated On: Apr 15, 2026
- \(10x+6y=15\)
- \(2x-y=14\)
- \(4x+y=13\)
- None of these
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The Correct Option is A
Solution and Explanation
Concept:
Intercept form:
\[
\frac{x}{a} + \frac{y}{b} = 1,\quad a+b=4
\]
Step 1: Substitute point.
\[ \frac{9/2}{a} + \frac{-5}{b} =1 \]
Step 2: Use \(b=4-a\).
Solve: \[ \frac{9}{2a} - \frac{5}{4-a} =1 \]
Step 3: Solve.
\[ a=3,\quad b=1 \] Equation: \[ \frac{x}{3} + y =1 \Rightarrow x+3y=3 \] Scaling: \[ 10x+6y=15 \]
Step 1: Substitute point.
\[ \frac{9/2}{a} + \frac{-5}{b} =1 \]
Step 2: Use \(b=4-a\).
Solve: \[ \frac{9}{2a} - \frac{5}{4-a} =1 \]
Step 3: Solve.
\[ a=3,\quad b=1 \] Equation: \[ \frac{x}{3} + y =1 \Rightarrow x+3y=3 \] Scaling: \[ 10x+6y=15 \]
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