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Algebra Difficulty: Easy

$f (x) = 4 x + b$

For the linear function $f$ , $b$ is a constant and $f left parenthesis 7 right parenthesis equals 28$ . What is the value of $b$ ?

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Explanation

Choice A is correct. For the linear function $f$ , it’s given that $f left parenthesis 7 right parenthesis equals 28$ . Substituting $7$ for $x$ and $28$ for $f (x)$ in the given function yields $28 = 4 (7) + b$ , or $28 = 28 + b$ . Subtracting $28$ from each side of this equation yields $0 equals b$ . Therefore, the value of $b$ is $0$ .

Choice B is incorrect. Substituting $1$ for $b$ in the given function yields $f (x) = 4 x + 1$ . For this function, when the value of $x$ is $7$ , the value of $f (x)$ is $29$ , not $28$ .

Choice C is incorrect. Substituting $4$ for $b$ in the given function yields $f (x) = 4 x + 4$ . For this function, when the value of $x$ is $7$ , the value of $f (x)$ is $32$ , not $28$ .

Choice D is incorrect. Substituting $7$ for $b$ in the given function yields $f (x) = 4 x + 7$ . For this function, when the value of $x$ is $7$ , the value of $f (x)$ is $35$ , not $28$ .