SAT Linear equations in two variables Practice Question 15 (Hard)

Question bank / Linear equations in two variables

Math · AlgebraHard

In the $xy$ -plane, line $m$ passes through the point $(-2, 5)$ and is perpendicular to the graph of $3x - 4y = 8$ . What is the $x$ -coordinate of the $x$ -intercept of line $m$ ?

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Answer: 7/4

The given line is $y = \frac{3}{4}x - 2$ , with slope $\frac{3}{4}$ , so line $m$ has slope $-\frac{4}{3}$ . Line $m$ : $y - 5 = -\frac{4}{3}(x + 2)$ . Set $y = 0$ : $-5 = -\frac{4}{3}(x + 2)$ , so $x + 2 = \frac{15}{4}$ and $x = \frac{7}{4}$ .

Using the parallel slope $\frac{3}{4}$ instead of the perpendicular slope gives $x = -\frac{26}{3}$ .

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