Linear functions SAT question

Math · Algebra · Easy · Answer it here, explanation included.

$x$	$f (x)$
$0$	$29$
$1$	$32$
$2$	$35$

For the linear function $f$ , the table shows three values of $x$ and their corresponding values of $f (x)$ . Which equation defines $f (x)$ ?

ExplanationShow

Choice A is correct. An equation that defines a linear function $f$ can be written in the form $f (x) = m x + b$ , where $m$ and $b$ are constants. It's given in the table that when $x = 0$ , $f (x) = 29$ . Substituting $0$ for $x$ and $29$ for $f (x)$ in the equation $f (x) = m x + b$ yields $29 = m (0) + b$ , or $29 = b$ . Substituting $29$ for $b$ in the equation $f (x) = m x + b$ yields $f (x) = m x + 29$ . It's also given in the table that when $x = 1$ , $f (x) = 32$ . Substituting $1$ for $x$ and $32$ for $f (x)$ in the equation $f (x) = m x + 29$ yields $32 = m (1) + 29$ , or $32 = m + 29$ . Subtracting $29$ from both sides of this equation yields $3 = m$ . Substituting $3$ for $m$ in the equation $f (x) = m x + 29$ yields $f (x) = 3 x + 29$ .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

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