linear function of weight change

Question

Suppose your dog weighed

1.6 pounds at birth and weighed

14pounds one year later. Based on these two data​ points, find a linear function that describes how weight varies with age. Use this function to predict your​ dog's weight at 4 and 11 years of age

Answer 1

Let years = x (independent variable) and weight = y (dependent variable)

In 0 years, the dog weighed 1.6lbs and in 1 year the dog weighed 14lbs, therefore you have two coordinates: (0, 1.6) = (x₁, y₁) and (1, 14) = (x₂, y₂) based on ----> (x, y)

Since the function that you find must be linear, it will be in the form of y = mx + b

Slope: m

m = (y₂ – y₁)/(x₂ – x₁)

m = (14 – 1.6)/(1 – 0)

m = 12.4/1 = 12.4

Y-Intercept: b

Your y intercept will always be the y-value of the coordinate where x = 0, so b = 1.6 (in other words, your starting point)

Therefore your function is y = 12.4x + 1.6

At 4 years old, x = 4

y = 12.4(4) +1.6 = 49.6 +1.6 = 51.2lbs

At 11 years old, x = 11

y = 12.4(11) + 1.6 = 136.4 +1.6 = 138lbs