The table gives the number of hours, h , of labor and a plumbers total charge f h , in

Question

The table gives the number of hours, h , of labor and a plumbers total charge f h , in dollars, for two different jobs. h f h 1 155 3 285 There is a linear relationship between h and f h . Which equation represents this relationship?

Accepted Answer

Choice C is correct. It's given that there is a linear relationship between a plumber's hours of labor, h , and the plumber's total charge f h , in dollars. It follows that the relationship can be represented by an equation of the form f h = m h + b , where m is the rate of change of the function f and b is a constant. The rate of change of f can be calculated by dividing the difference in two values of f h by the difference in the corresponding values of h . Based on the values given in the table, the rate of change of f is 285 - 155 3 - 1 , or 65 . Substituting 65 for m in the equation f h = m h + b yields f h = 65 h + b . The value of b can be found by substituting any value of h and its corresponding value of f h for h and f h , respectively, in this equation. Substituting 1 for h and 155 for f h yields 155 = 65 1 + b , or 155 = 65 + b . Subtracting 65 from both sides of this equation yields 90 = b . Substituting 90 for b in the equation f h = 65 h + b yields f ( h ) = 65 h + 90 . Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

$h$	$f (h)$
$1$	$155$
$3$	$285$

Question 898164