Question

fluency and skills practice name:
lesson 16
interpreting a linear function continued
3 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 wont 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?
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grade 8 • lesson 16 page 2 of 2

Explanation:

a. In the linear equation for total cooking time, the variable with the coefficient is the input (turkey weight), and the other is the total output. We use "is a function of" to link total time to weight.
b. The constant term in a linear function $y=mx+b$ is the fixed value when the input is 0, here the set cooking time for the macaroni and cheese.
c. The coefficient of $x$ (rate of change) is the per-pound cooking time for the turkey, as it changes with the turkey's weight.
d. The turkey's cooking time uses the variable term of the equation; substitute the given weight into this term.

Answer:

a. $x$ represents the weight of the turkey in pounds, and $y$ represents the total cooking time in minutes. Total cooking time $y$ is a function of the turkey's weight $x$.
b. The value 40 represents the fixed cooking time (in minutes) required for the macaroni and cheese, which does not depend on the turkey's weight.
c. The rate of change (15) represents the number of minutes of cooking time required per pound of turkey.
d. The total cooking time for just the 12-pound turkey is 180 minutes. This is found by calculating the variable part of the equation: $15 \times 12 = 180$ minutes, as this term accounts for the turkey's cooking time.