SAT Linear equations in two variables Practice Question 11 (Medium)

Question bank / Linear equations in two variables

Math · AlgebraMedium

Line $\ell$ in the $xy$ -plane is defined by $6x - 3y = 9$ . Which equation defines a line perpendicular to line $\ell$ ?

$2x - y = 4$

$x - 2y = 7$

$2x + y = 7$

$x + 2y = 7$

Show answer and explanation

Answer: D

Rewrite $\ell$ : $y = 2x - 3$ , so its slope is 2. A perpendicular line has slope $-\frac{1}{2}$ . For $x + 2y = 7$ , $y = -\frac{1}{2}x + \frac{7}{2}$ , which has slope $-\frac{1}{2}$ .

Choice A has slope 2, which makes it parallel to $\ell$ , not perpendicular.

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