Question

In class, Julie was asked to create a scenario for the linear function shown. She came up with the following:

Joe planned a hiking trip from where he parked his car to the mountain cabin he had rented. Joe parked 12 miles away from the cabin. After one hour, he was still 7 miles from the cabin. Joe’s hike from his car to the cabin can be modeled by the function f(x)=-3x+12.

Does Julie’s scenario match the linear function graphed? If not, where does she go wrong? How can she correct her mistake and match scenario to the function?

Answer 1

The linear function that matches Julie's scenario is

`y=-5x+12`

Explanation:

see the attached figure to better understand the problem

Let

x -----> the time in hours

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

we know that

After one hour, he was still 7 miles from the cabin.

so

For x=1 h, y=7 mi

Observing the graph

For x=1 h, y=9 mi

therefore

Julie's scenario does not match the graphed linear function.

Find the correct linear equation that match Julie’s scenario

we have the points

(0,12) and (1,7)

Find the slope

`m=(7-12)/(1-0)=-5`

Find the linear equation in slope intercept form

`y=mx+b`

we have

`m=-5`

`b=12` ----> the y-intercept is the point (0,12)

substitute

`y=-5x+12`

therefore

The linear function that matches Julie's scenario is

`y=-5x+12`