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The table shows the relationship between calories and fat grams contained in orders of French fries from various restaurants.

Calories
Fat Grams
240
14
280
15
310
16
260
12
340
16
350
18
300
13

Assuming the data can best be described by a linear model, how many fat grams would be expected to be contained in a 315-calorie order of French fries?

F 15 fat grams

G 16 fat grams

H 17 fat grams

J 18 fat grams

Short Answer

Expert verified

Option F is the correct answer.

Step by step solution

01

Step 1. Define a variable.

A variable in Mathematics is defined as the alphabetic character that expresses a numerical value or a number.

02

Step 2. Define an equation.

In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the sign "=".

03

Step 3. Complete the number of fat grams to be expected in a 315-calorie order of French fries.

Assume the data can best be described by a linear model.

Let the linear equation is

y=ax+b           ........1.

Where,

y=The number of fat grams

x=The number of calories

aand bare the constants.

Observe the table.

Atx=260,y=12

Use equation (1).

12=260a+b          ........2

Atx=340,y=16

Use equation (1).

16=340a+b       .........3

Subtract (2) from (3).

4=80aa=480a=120

Substitute a=120in equation (2).

12=260120+b      12=13+bb=1213b=1

Substitute a=120and b=1, in equation (1).

y=120x+1y=120x1         ........4

Now, substitute x=315in equation (4).

y=1203151y=15.751y=14.75y15

Hence, 15 fat grams would be expected in a 315-calorie order of French fries.

Therefore, option F is the correct answer.

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