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Algebra / Linear functions Difficulty: Easy

Area (square feet)	Water (gallons)
$2,520$ $2,520$	$4,536$ $4,536$
$3,780$ $3,780$	$6,804$ $6,804$
$5,040$ $5,040$	$9,072$ $9,072$

The buildings of a shopping center are designed to allow water to drain from the roof into gutters on the sides of the buildings. The table shows the relationship between the area $x$ $x$ , in square feet, of a roof and the amount of water $f (x)$ $f (x)$ , in gallons, drained from the roof into the gutters over a certain period of time. Which equation could define $f$ $f$ ?

$f left parenthesis x right parenthesis equals 0.6 x$

$f left parenthesis x right parenthesis equals 1.8 x$

$f left parenthesis x right parenthesis equals 2,268 x$

$f left parenthesis x right parenthesis equals 4,536 x$

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Explanation

Choice B is correct. It's given that the table represents the relationship between the area $x$ $x$ , in square feet, of the roof of a shopping center and the amount of water $f (x)$ $f (x)$ , in gallons, drained from the roof into the gutters. Every choice represents this relationship with an equation defining $f$ $f$ in the form $f (x) = m x$ $f (x) = m x$ , where $m$ $m$ is a constant rate of change. The value of $m$ $m$ can be determined by dividing both sides of the equation by $x$ $x$ . Each of three pairs of $x$ $x$ and $f (x)$ $f (x)$ in the table yield $m = 1.8$ $m equals 1.8$ , since $\frac{4,536}{2,520} = 1.8$ $\frac{4,536}{2,520} = 1.8$ , $\frac{6,804}{3,780} = 1.8$ $\frac{6,804}{3,780} = 1.8$ , and $\frac{9,072}{5,040} = 1.8$ $\frac{9,072}{5,040} = 1.8$ . Therefore, the equation $f (x) = 1.8 x$ $f left parenthesis x right parenthesis equals 1.8 x$ could define $f$ $f$ .

Choice A is incorrect. For the roof with an area of $2,520$ $2,520$ square feet, this equation would yield $0.6 (2,520)$ $0.6 left parenthesis 2,520 right parenthesis$ , or $1,512$ $1,512$ , gallons, not the $4,536$ $4,536$ gallons shown in the table.

Choice C is incorrect. For the roof with an area of $2,520$ $2,520$ square feet, this equation would yield $2,268 (2,520)$ $2,268 left parenthesis 2,520 right parenthesis$ , or $5,715,360$ $5,715,360$ , gallons, not the $4,536$ $4,536$ gallons shown in the table.

Choice D is incorrect. For the roof with an area of $2,520$ $2,520$ square feet, this equation would yield $4,536 (2,520)$ $4,536 left parenthesis 2,520 right parenthesis$ , or $11,430,720$ $11,430,720$ , gallons, not the $4,536$ $4,536$ gallons shown in the table.