16Hit1600
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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