Question

interpreting a linear function continued
1 amber plans to cook a turkey and macaroni and cheese for a special dinner. since she will need to use the oven for both dishes, and they won’t both fit in the oven at the same time, she has to determine how much time all the cooking will take. the macaroni and cheese will take a set amount of time, while the turkey takes a certain number of minutes per pound that the turkey weighs.
the equation models the total cooking time amber will need to prepare her dishes.

$y = 15x + 40$

a. what do variables $x$ and $y$ represent? use the phrase is a function of to describe how the two quantities relate to each other.

b. what does the value 40 represent?

c. what does the rate of change represent?

d. what is the total cooking time for just the turkey if it weighs 12 pounds? how do you know?

Explanation:

Part a

In the context of cooking time, \( x \) should represent the weight of the turkey (in pounds) because the turkey's cooking time depends on its weight (it takes a certain number of minutes per pound). \( y \) represents the total cooking time (in minutes) for both dishes. So total cooking time (\( y \)) is a function of the turkey's weight (\( x \)).

The equation is in slope - intercept form \( y=mx + b \), where \( b \) is the y - intercept. In the context of cooking, the macaroni and cheese takes a set amount of time. When \( x = 0 \) (a turkey with 0 pounds, which doesn't make sense in reality, but in the equation's context), \( y=40 \). So 40 represents the cooking time (in minutes) for the macaroni and cheese (the fixed time for that dish).

In the linear equation \( y = mx + b \), \( m \) is the rate of change (slope). Here, \( m = 15 \). Since \( x \) is the weight of the turkey (in pounds) and \( y \) is the total cooking time (in minutes), the rate of change of 15 means that for each additional pound the turkey weighs, the total cooking time increases by 15 minutes. So it represents the number of minutes it takes to cook one pound of the turkey.

Answer:

\( x \) represents the weight of the turkey (in pounds), \( y \) represents the total cooking time (in minutes), and \( y \) is a function of \( x \) (i.e., \( y = 15x + 40 \) means total cooking time is a function of the turkey's weight).

Part b