SAT Linear equations in two variables Practice Question 17 (Hard)

Question bank / Linear equations in two variables

Math · AlgebraHard

In the $xy$ -plane, a line with a slope of $3$ passes through the points $(p, 4)$ and $(6, p)$ , where $p$ is a constant. What is the value of $p$ ?

$\frac{11}{4}$

$7$

$\frac{11}{2}$

$22$

Show answer and explanation

Answer: C

Use the slope formula: $\frac{p - 4}{6 - p} = 3$ . Then $p - 4 = 18 - 3p$ , so $4p = 22$ and $p = \frac{11}{2}$ .

Choice B comes from subtracting the $y$ -values in the opposite order from the $x$ -values, writing $\frac{4 - p}{6 - p} = 3$ .

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