The graph of the linear function f in the xy-plane has a... | SAT Linear functions Question, Answer Explained

Math · AlgebraEasy

The graph of the linear function $f$ in the $xy$ -plane has a slope of $-3$ and passes through the point $(0, 8)$ . Which equation defines $f$ ?

$f(x) = -3x - 8$

$f(x) = 3x + 8$

$f(x) = 8x - 3$

$f(x) = -3x + 8$

Show answer and explanation

Answer: D

A linear function can be written as $f(x) = mx + b$ , where $m$ is the slope and $b$ is the $y$ -coordinate of the $y$ -intercept. Here $m = -3$ and $b = 8$ , so $f(x) = -3x + 8$ .

Choice C switches the slope and the $y$ -intercept.

Why the other choices are wrong

A. The point (0, 8) means f(0) = 8, but this function gives f(0) = -8.
B. This function has a slope of 3, not -3.
C. This switches the two numbers: it has a slope of 8 and a y-intercept of -3.

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, or take a free full-length practice test.