AlgebraHardy-intercept of a line parallel to a given line through a point
Algebra practice question
In the xy-plane, line m is parallel to the line 3x + 2y = 8 and passes through the point (4, 5). What is the y-intercept of line m?
Answer: 11
The line 3x + 2y = 8 has slope −3/2, so line m does too. Through (4, 5): 5 = −(3/2)(4) + b → 5 = −6 + b → b = 11.
Common wrong answers
- If you answered 4
- 4 is the y-intercept of the given line (8 ÷ 2), not of line m.
- If you answered 8
- 8 comes from using a slope of 3/2 instead of −3/2 and a sign slip.
- If you answered -1
- −1 comes from 5 = 6 + b, dropping the sign of the slope.
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