Algebra practice question

Answer: 6

Parallel lines have equal slopes. The second line is y = −2x + 2, slope −2. The first is y = (−a/3)x + 2, slope −a/3. Setting −a/3 = −2 gives a = 6. (Then the first line is y = −2x + 2 — the same line, which is the parallel case with infinitely many common points; any other a gives a single intersection.)

Common wrong answers

If you answered 2

2 matches the x-coefficients, but slopes depend on the ratio of the x- and y-coefficients: a/3 must equal 2/1.

If you answered 3

3 gives slope −1, not −2.

If you answered -6

−6 gives slope +2, the negative of what's needed.

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