What is the slope of line perpendicular to y = −3x + 7?
- (a)−1⁄3
- (b)3
- (c)1⁄3
- (d)−3
Answer
Why
Correct — C. Read the slope from y = mx + c, then take its negative reciprocal.
Given line: y = −3x + 7, so m₁ = −3
Perpendicular condition: m₁ × m₂ = −1
Substitute: −3 × m₂ = −1
Divide by −3: m₂ = 1⁄3 → option (c)
Why the others are wrong
- (a)−1⁄3 — −1⁄3 flips the fraction but keeps the sign. −3 × (−1⁄3) = +1, not −1, so the two lines are not perpendicular.
- (b)3 — 3 changes the sign but not the fraction. −3 × 3 = −9, not −1, so a line of slope 3 is not perpendicular to this one.
- (d)−3 — −3 is the given line's own slope. Equal slopes make lines parallel, and −3 × (−3) = 9, not −1.
Concept
In y = mx + c, m is the slope and c the y-intercept, so y = −3x + 7 falls 3 units for every unit to the right.
Two lines, neither vertical, are perpendicular when m₁ × m₂ = −1, so the perpendicular slope is −1⁄m₁. Parallel lines share a slope. The intercept, +7, plays no part in either test.
The product rule m₁ × m₂ = −1 breaks down only for a vertical line, whose slope is undefined, paired with a horizontal one. y = −3x + 7 is neither, so the rule applies directly.
Key facts
- In y = mx + c, the slope is m and the y-intercept is c.
- Perpendicular lines, neither vertical: m₁ × m₂ = −1.
- Parallel lines have equal slopes.
- For ax + by + c = 0, the slope is −a⁄b.
Study next
Common traps
- Taking the reciprocal but keeping the sign, which gives −1⁄3.
- Answering with −3, the slope of a parallel line, not a perpendicular one.
The same negative reciprocal drives 17 Sep 2025, 16:00, Quant Q.19: the segment from (2, 8) to (6, 4) has slope −1, so its perpendicular bisector has slope 1 and, through the midpoint (4, 6), is y = x + 2.
17 Sep 2025, 16:00, Quant Q.16 asks only for the slope through (2, 3) and (4, 7): (7 − 3) ⁄ (4 − 2) = 2.
Related PYQs
No directly related past PYQ was found.