AlgebraVery hardIntercept from an enclosed area
Algebra practice question
In the xy-plane, the line y = −2x + b, where b is a positive constant, forms a triangle with the two axes. If the area of that triangle is 16, what is the value of b?
Answer: 8
The intercepts are (b/2, 0) and (0, b), so the area is (1/2)(b/2)(b) = b²/4. Setting b²/4 = 16 gives b = 8.
Common wrong answers
- If you answered 4
- 4 solves b²/4 = 16 as b/4 = 16 wrongly, or halves 8.
- If you answered 16
- 16 is the area, not b.
- If you answered 5.66
- 5.66 is √32, from an area formula without the half.
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