Question

For the first 3 years of a horse's life, the weight, w (in kilograms), of the horse approximately fits the formula w(t)=30+170t, where t is the age of the horse in years. Which of the following is the most accurate interpretation of the slope of the line represented by this formula?

A. The slope is 170. This means that the horse gains an average of 170 kilograms per year for the first 3 years of its life.
B. The slope is 30. This means that the horse gains a total of 30 kilograms in the first 3 years of its life.
C. The slope is 30. This means the horse gains on average 30 kilograms per use for the first 3years of its life.
D. The slope is 170. This means that the horse gains a total of 170 kilograms in the first 3 years of its life.

Answer 1

Option A. The slope is 170. This means that the horse gains an average of 170 kilograms per year for the first 3 years of its life

Explanation:

Let

t ----> the number of years

w ---> is the weight in kilograms of the horse

we know that

The equation of a line in slope intercept form is equal to

`y=mx+b`

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value

In this problem we have

`w(t)=30+170t`

where

The slope or unit rate is equal to

`m=170\ (kg)/(year)` ---> (for the first 3 years of a horse's life)

The y-intercept is equal to

`b=30\ kg` ---> value of w when the value of t is equal to zero

therefore

The slope is 170. This means that the horse gains an average of 170 kilograms per year for the first 3 years of its life