Which of the following is the equation of the line through \((-2,\,5)\) that is parallel to the line \(3x-y=4\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(3x-y=-11\)
Parallel lines have equal slopes. Lines \(3x-y=c\) all have the same slope as \(3x-y=4\) (only the constant changes), so the required line is \(3x-y=c\) and the given point fixes \(c\).
Slope of \(3x-y=4\): \(y=3x-4\), so the slope is \(3\)
Required line: \(3x-y=c\)
It passes through \((-2,\,5)\): \(c=3(-2)-5=-11\)
Equation: \(3x-y=-11\)
Why the other options are incorrect
Option (1) \(x+3y=13\) — Incorrect. It passes through \((-2,\,5)\), but its slope is \(-\frac{1}{3}\), not \(3\).
Option (2) \(3x-y=11\) — Incorrect. It is parallel, but at \((-2,\,5)\) the left side is \(-11\), not \(11\).
Option (4) \(x-3y=-17\) — Incorrect. It passes through \((-2,\,5)\), but its slope is \(\frac{1}{3}\), not \(3\).