sat suite question viewer

Algebra / Linear functions Difficulty: Easy

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

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 $x$ , in square feet, of a roof and the amount of water $f (x)$ , in gallons, drained from the roof into the gutters over a certain period of time. Which equation could define $f$ ?

$f left parenthesis x right parenthesis equals 0.6 x$

$f left parenthesis x right parenthesis equals 1.8 x$

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

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

Back question 150 of 152 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152

Explanation

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

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

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

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