sat suite question viewer

Algebra / Linear functions Difficulty: Medium

The figure presents a 3-column table, with 3 rows of data, titled “Energy per Gram of Typical Macronutrients.” The heading for column 1 is “Macronutrient,” the heading for column 2 is “Food calories,” and the heading for column 3 is “Kilojoules.” The 3 rows of data are as follows. Row 1.Macronutrient, Protein; Food calories, 4 point zero; Kilojoules, 16 point 7. Row 2. Macronutrient, Fat; Food calories, 9 point zero; Kilojoules, 37 point 7. Row 3. Macronutrient, Carbohydrate; Food calories, 4 point zero; Kilojoules, 16 point 7.

The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food. If x food calories is equivalent to k kilojoules, of the following, which best represents the relationship between x and k ?

 

Back question 56 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. The relationship between x food calories and k kilojoules can be modeled as a proportional relationship. Let the ordered pair x sub 1 comma k sub 1 and the ordered pair x sub 2 comma k sub 2 represent the values in the first two rows in the table: the ordered pair 4 point 0 comma 16 point 7 and the ordered pair 9 point 0 comma 37 point 7. The rate of change, or the fraction with numerator, k sub 2 minus k sub 1, and denominator x sub 2 minus x sub 1, end fraction, is 21 over 5 equals 4 point 2; therefore, the equation that best represents the relationship between x and k is k equals 4 point 2 x.

Choice A is incorrect and may be the result of calculating the rate of change using the fraction with numerator, x sub 2 minus x sub 1, and denominator k sub 2 minus k sub 1, end fraction. Choice C is incorrect because the number of kilojoules is greater than the number of food calories. Choice D is incorrect and may be the result of an error when setting up the equation.