Domain, Slope and Y-intercept of a Function

Question

According to Betty a 2 lb. tenderloin roast put in the oven at 425 degrees will take 45 minutes to cook to medium doneness. A 4 lb. tenderloin at the same temperature will take an hour to reach medium doneness.

a. write a function that models time it takes a tenderloin to roast in terms of the weight of the roast.

b. what is the slope of this function?

c. what is the y-intercept?

d. if a roast weighs 3 lb. how long will it take to cook?

e. if a roast takes 1 hour and 20 minutes to roast, how much does it weigh?

f. what is a reasonable domain for your function?

Answer 1

T = F(w) where T is the time in minutes and w is the weight in pounds

45 = F(2)

60 = F(4)

the slope is (60-45)/(4-2) = 15/2 = 7.5

7.5 minutes per pound

B = y - mx = 60 - (7.5)(4) = 60 - 30 = 30

F(w) = 7.5 * w + 30

F(3) = 7.5 * 3 + 30 = 22.5 + 30 = 52.5

1 hour and 20 minutes = 80 minutes

80 = 7.5*w + 30

50 = 7.5 * w

500 = 75 w

w = 500/75 = 20/3 = 6 and 2/3 lb