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Linear Equations in One Variable

SAT Math· difficulty 5/5

Lines ℓ1\ell_1: ax+2y=6ax + 2y = 6 and ℓ2\ell_2: 3x−y=43x - y = 4 are perpendicular. What is the value of aa?

  • A

    −23-\frac{2}{3}

  • B

    −6-6

  • C

    6

  • D

    23\frac{2}{3}

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Explanation

Slope of ℓ2\ell_2 is 33. So slope of ℓ1\ell_1 must be −13-\frac{1}{3}. From ℓ1\ell_1: slope =−a2= -\frac{a}{2}. Set −a2=−13-\frac{a}{2} = -\frac{1}{3}: a=23a = \frac{2}{3}.

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