The table below gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food. | Energy per Gram of Typical Macronutrients | Food calories | Kilojoules | |---|---|---| | Protein | 4.0 | 16.7 | | Fat | 9.0 | 37.7 | | Carbohydrate | 4.0 | 16.7 | If food calories is equivalent to kilojoules, which of the following best represents the relationship between and ?

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SAT Linear Functions Question 32 | Free SAT Prep | Aniko

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Question 32·Medium·Linear Functions

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The table below gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food.

Energy per Gram of Typical Macronutrients	Food calories	Kilojoules
Protein	4.0	16.7
Fat	9.0	37.7
Carbohydrate	4.0	16.7

If $x$ food calories is equivalent to $k$ kilojoules, which of the following best represents the relationship between $x$ and $k$ ?

For table-based conversion questions, first decide which quantity depends on the other (here, kilojoules depend on calories), then compute the constant ratio output/input from any row (kilojoules ÷ calories). Confirm the ratio is consistent across rows, and finally choose the equation where the dependent variable equals this constant times the independent variable, checking that the units align with the table (k should be a multiple of x, not the other way around).

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Focus on a single row first

Look at just one macronutrient in the table, such as protein. How many kilojoules go with 4.0 food calories?

Think in terms of a per-1 rate

Use the protein row to find how many kilojoules correspond to 1 food calorie. What do you get if you divide the kilojoules value by the food calories value?

Use the constant rate to build an equation

Once you know about how many kilojoules correspond to 1 food calorie, ask: if there are x food calories, how many kilojoules would that be? Which variable should be the product of the other variable and the constant rate?

Desmos Guide

Compute the conversion factor

In Desmos, type 16.7/4 and also 37.7/9 on separate lines. Notice that both values are close to the same number (about 4.2). This number is the number of kilojoules per food calorie, so any correct equation must multiply x by this constant to get k.

Step-by-step Explanation

Identify what x and k represent

The problem says that $x$ is the number of food calories and $k$ is the equivalent number of kilojoules. The table shows how many kilojoules go with each calorie for different macronutrients (protein, fat, carbohydrate). We are looking for a conversion relationship that always turns calories into kilojoules.

Find the kilojoules per food calorie from the table

Pick any row of the table. For protein, 4.0 food calories correspond to 16.7 kilojoules.

Compute the ratio of kilojoules to food calories:

$16.7/4.0 = 4.175$ (about $4.2$ ).

That means there are about $4.2$ kilojoules for each 1 food calorie.

Check that the ratio is consistent

To be sure the conversion is the same for all macronutrients, check another row. For fat, 9.0 food calories correspond to 37.7 kilojoules.

Compute the ratio again:

$37.7/9.0 \approx 4.19$ (also about $4.2$ ).

So, the number of kilojoules is always about $4.2$ times the number of food calories, no matter which macronutrient you use.

Write the equation relating k and x

If each food calorie gives about $4.2$ kilojoules, then for $x$ food calories, the kilojoules $k$ are found by multiplying $x$ by $4.2$ .

So the relationship is:

$k = 4.2x$ .

This matches answer choice B.

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Step-by-step Explanation

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Step-by-step Explanation