x f ( x ) 0 29 1 32 2 35 For the linear function f , the table shows

Question

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 ) ?

Accepted Answer

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.

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

Question 79c4d3