SAT Linear equations in two variables Practice Question 9 (Medium)

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Question bank / Linear equations in two variables

Math · AlgebraMedium

A line in the $xy$ -plane passes through the points $(2, -1)$ and $(6, 7)$ . Which equation represents the line?

$x - 2y = 4$

$2x - y = -5$

$2x + y = 3$

$2x - y = 5$

Show answer and explanation

Answer: D

The slope is $\frac{7 - (-1)}{6 - 2} = 2$ , so $y = 2x + b$ . Using $(2, -1)$ : $-1 = 4 + b$ , so $b = -5$ and $y = 2x - 5$ , which is $2x - y = 5$ . Check $(6, 7)$ : $12 - 7 = 5$ .

Choice A passes through $(2, -1)$ but not through $(6, 7)$ , since $6 - 14 = -8$ .

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