For the linear function f, the graph of y = f(x) in the xy -plane has a slope of -5 and passes through the point (2, -4). Which equation defines f?

For the linear function f, the graph of y = f(x) in the xy -plane has a slope of -5 and... | SAT Linear functions Practice

Context: The graph of the linear function $f$ has slope $-5$ and passes through $(2, -4)$ . We need the equation that defines $f$ .

Answer: D) $f(x) = -5x + 6$

Why? Start from $f(x) = -5x + b$ . The point says $f(2) = -4$ , so $-5(2) + b = -4$ , giving $-10 + b = -4$ and $b = 6$ . Hence $f(x) = -5x + 6$ , and $-5(2) + 6 = -4$ checks out.

Traps:

A) $f(x) = 2x - 4$ reuses the coordinates of the point as slope and intercept, discarding the stated slope of $-5$ ; it gives $f(2) = 0$ .
B) $f(x) = -5x - 4$ takes the $y$ -coordinate $-4$ as the intercept, but $-4$ is the output at $x = 2$ , not at $x = 0$ ; it gives $f(2) = -14$ .
C) $f(x) = -5x - 5$ reuses the slope as the constant term as well; it gives $f(2) = -15$ .

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Question Bank

SAT Linear functions practice question

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