Question bank / Linear equations in two variables

Math · AlgebraMedium

A line in the xyxy-plane passes through the points (−1,4)(-1, 4) and (3,−8)(3, -8). The equation of the line can be written as y=mx+by = mx + b, where mm and bb are constants. What is the value of m+bm + b?

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Answer: -2

The slope is m=−8−43−(−1)=−124=−3m = \frac{-8 - 4}{3 - (-1)} = \frac{-12}{4} = -3. Substitute (−1,4)(-1, 4): 4=−3(−1)+b=3+b4 = -3(-1) + b = 3 + b, so b=1b = 1. Then m+b=−3+1=−2m + b = -3 + 1 = -2.

Treating −3(−1)-3(-1) as −3-3 gives b=7b = 7 and m+b=4m + b = 4.

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