16Hit1600
AlgebraHardIntercept from a known crossing point

Algebra practice question

The functions f and g are defined by f(x) = 2x + b and g(x) = −x + 7, where b is a constant. If the graphs of f and g in the xy-plane intersect at the point where x = 2, what is the value of b?

Answer: 1

At x = 2, g(2) = −2 + 7 = 5. For the graphs to meet there, f(2) = 5 too: 2(2) + b = 5, so b = 1.

Common wrong answers

If you answered 3
3 comes from 2 + b = 5, forgetting to multiply the slope by 2.
If you answered 5
5 is the shared y-value at the intersection, not b.
If you answered -1
−1 has the wrong sign: 4 + b = 5 gives b = 1.

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