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Algebra / Linear functions Difficulty: Medium

$x$ $x$	$10$ $10$	$15$ $15$	$20$ $20$	$25$ $25$
$f (x)$ $f (x)$	$82$ $82$	$137$ $137$	$192$ $192$	$247$

The table shows four values of $x$ and their corresponding values of $f (x)$ . There is a linear relationship between $x$ and $f (x)$ that is defined by the equation $f (x) = m x - 28$ , where $m$ is a constant. What is the value of $m$ ?

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Explanation

The correct answer is $11$ . It's given that $f (x)$ is defined by the equation $f (x) = m x - 28$ , where $m$ is a constant. It's also given in the table that when $x equals 10$ , $f left parenthesis x right parenthesis equals 82$ . Substituting $10$ for $x$ and $82$ for $f (x)$ in the equation $f (x) = m x - 28$ yields, $82 = m (10) - 28$ . Adding $28$ to both sides of this equation yields $110 equals 10 m$ . Dividing both sides of this equation by $10$ yields $11 equals m$ . Therefore, the value of $m$ is $11$ .