SAT Linear functions Practice Question 10 (Medium)

Math · AlgebraMedium

The graph of the linear function $f$ in the $xy$ -plane has an $x$ -intercept at $(6, 0)$ and a $y$ -intercept at $(0, -4)$ . Which equation defines $f$ ?

$f(x) = \frac{2}{3}x - 4$

$f(x) = -\frac{2}{3}x - 4$

$f(x) = \frac{3}{2}x - 4$

$f(x) = -4x + 6$

Show answer and explanation

Answer: A

The slope is $\frac{0 - (-4)}{6 - 0} = \frac{4}{6} = \frac{2}{3}$ . The $y$ -intercept is $-4$ , so $f(x) = \frac{2}{3}x - 4$ . Check: $f(6) = 4 - 4 = 0$ .

Choice C inverts the slope, computing change in $x$ over change in $y$ .

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