Question

HELP!

The equation shown is a model developed by a researcher, where x represents the height, in inches, of a 36-month-old boy, and y represents his maximum height, in inches, as an adult.
y= 3.5x - 60
Part A
A 36-month-old boy has a height of 36 inches. Based on the model, what is his expected height, in inches, as an adult?
Answer:

Part B
Jack and Kris are 36-month-old boys. Jack is exactly 1 inch taller than Kris.

Based on the model, how many inches taller is Jack expected to be than Kris is expected to be when they are adults?
Answer:

Part C
An adult male has a height of 73 inches. Based on the model, what was his height, in inches, when he was 36 months old?

Part D
Bill and Ryan are adult males. Bill is exactly 10.5 inches taller than Ryan. Based on the model, how many inches taller was Bill than Ryan when they were 36 months old?

Answer 1

A) 66 inches

B) 3.5 inches

C) 38 inches

D) 3 inches

Explanation:

A)

If the height of the 36-month-old boy is 36 inches, we just need to use the value of x = 36 in the equation, and then find the value of y:

y = 3.5 * 36 - 60 = 66 inches

B)

As the slope of the equation is 3.5, an increase of 1 in the value of x causes a increase of 3.5 in the value of y, so the answer is 3.5 inches.

C)

We just need to use y = 73 and then find x:

73 = 3.5x - 60

3.5x = 133

x = 38 inches

D)

If the increase in y was 10.5, we just need to divide this value by the slope to find the increase in x:

dx = dy/3.5 = 10.5/3.5 = 3 inches