AlgebraMediumUnknown intercept from a known intersection
Algebra practice question
In the xy-plane, the lines y = 3x + b and y = −x + 8 intersect at a point whose x-coordinate is 1, where b is a constant. What is the value of b?
Answer: 4
At x = 1 the second line gives y = 7. The first line must pass through (1, 7): 7 = 3(1) + b, so b = 4.
Common wrong answers
- If you answered 7
- 7 is the y-coordinate of the intersection, not b.
- If you answered 10
- 10 comes from 7 = −3 + b, using the wrong sign on the slope.
- If you answered -4
- −4 comes from 3 = 7 + b.
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