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?

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calculista calculista · Answer 1 · 2019-10-04T12:52:43+02:00

Answer:

The linear function that matches Julie's scenario is

[tex]y=-5x+12[/tex]

Step-by-step 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

[tex]m=(7-12)/(1-0)=-5[/tex]

Find the linear equation in slope intercept form

[tex]y=mx+b[/tex]

we have

[tex]m=-5[/tex]

[tex]b=12[/tex] ----> the y-intercept is the point (0,12)

substitute

[tex]y=-5x+12[/tex]

therefore

The linear function that matches Julie's scenario is

[tex]y=-5x+12[/tex]