SAT Linear functions Practice Question 18 (Hard)

Math · AlgebraHard

The graph of the linear function $f$ in the $xy$ -plane passes through the points $(a, 2a)$ and $(3a, -4a)$ , where $a$ is a nonzero constant. Which of the following is the $x$ -intercept of the graph?

$\left(\frac{5a}{3}, 0\right)$

$(5a, 0)$

$\left(-\frac{5a}{3}, 0\right)$

$\left(\frac{2a}{3}, 0\right)$

Show answer and explanation

Answer: A

The slope is $\frac{-4a - 2a}{3a - a} = \frac{-6a}{2a} = -3$ . Using point-slope form, $f(x) = -3(x - a) + 2a = -3x + 5a$ . Setting $f(x) = 0$ gives $x = \frac{5a}{3}$ .

Choice B is the $y$ -intercept value $5a$ , not the $x$ -intercept.

Ask Owl about this question Next question

Got it wrong? On SAT Owl, Owl looks at the answer you chose and explains the exact mistake, then gives you similar questions until it sticks. Get your predicted SAT score free.