Algebra practice question

Answer: 7

Parallel lines have equal slopes, so line m has slope −3 and its equation is y = −3x + b. Substituting the point (2, 1): 1 = −3(2) + b, so 1 = −6 + b and b = 7. Common errors: using the perpendicular slope 1/3 instead of −3 (which would give b = 1/3), reusing the y-intercept 5 of the given line, or sign-flipping the substitution to get 1 = 6 + b and b = −5.

Common wrong answers

If you answered 5

You reused the y-intercept of the given line; parallel lines share the slope (−3), not the intercept, so you still need to substitute (2, 1) to find b.

If you answered -5

You sign-flipped the substitution, writing 1 = 6 + b instead of 1 = −3(2) + b = −6 + b; with the correct sign, b = 7.

If you answered 1/3

You used the perpendicular slope 1/3 instead of the parallel slope −3; parallel lines have equal slopes, so line m has slope −3.

If you answered -3

That's the slope of line m, but the question asks for b, the y-intercept: substitute (2, 1) into y = −3x + b to get b = 7.

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