Question

1. What is the slope for section "d" of Mrs. Washington's commute.

2. What does it mean that the slope is negative in context of the problem?

3. Why are the slopes different over different intervals?

4. How long does it take Mrs. Washington to get home? How did you know this?

Answer 1

Part 1) The slope for section "d" is
`m=-0.5\ mi/min`

Part 2) see the explanation

Part 3) see the explanation

Part 4) Mrs. Washington get home in 32 minutes (see the explanation)

Explanation:

Part 1) What is the slope for section "d" of Mrs. Washington's commute

Let

x ----> the time in minutes

y ----> the distance from home in miles

we know that

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

we have the points (look at the graph)

(22,5) and (32,0)

substitute

`m=(0-5)/(32-22)`

`m=(-5)/(10)=-0.5\ mi/min`

The slope represent the speed

Part 2) What does it mean that the slope is negative in context of the problem?

we know that

The slope is negative because we have a decreasing function

As the value of x increases the value of y decreases

In the context of the problem

As time passes, the distance from home decreases

Part 3) Why are the slopes different over different intervals?

we know that

In this problem

The slope or unit rate is the same as the speed of the car

so

If the slopes are different over different intervals, it's because the speeds are different over different intervals

Part 4) How long does it take Mrs. Washington to get home? How did you know this?

we know that

When Mrs. Washington get home, the value of the distance from home must be equal zero (x-intercept)

Remember that

The x-intercept is the value of x when the value of y is equal to zero

In context of the problem, the x-intercept is the time when Mrs. Washington get home (the distance from home is equal to zero)

Looking at the graph

For y=0

The value of x=32 minutes

The x-intercept is (32,0)

therefore

Mrs. Washington get home in 32 minutes