Line k is perpendicular to the line y = (2/3)x + 1 and passes through the point (4, −1). What is the y-intercept of line k?

Question

Accepted Answer

A. 5. Perpendicular lines have slopes that are negative reciprocals, so line k has slope −3/2. Then −1 = (−3/2)(4) + b, so −1 = −6 + b and b = 5.

Answer

B. −7 — You flipped the fraction but kept the sign, using slope 3/2: −1 = 6 + b gives b = −7. A perpendicular slope is the NEGATIVE reciprocal.

Answer

C. −11/3 — You used the same slope, 2/3, which gives a PARALLEL line: −1 = 8/3 + b, b = −11/3. Perpendicular means flip AND negate.

Answer

D. 5/3 — You negated the slope but didn't flip it, using −2/3: −1 = −8/3 + b gives b = 5/3. The reciprocal of 2/3 is 3/2.

Algebra practice question