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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?

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 ca class=

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Answer:

1. Julie’s scenario doesn't match the linear function graphed, because the graphed function is f(x)=-3x+12 and must be f(x)=-5x+12

2. She has counted the slope of the line incorrect.

3. She can write f(x)=-5x+12 and draw the line with the x-intercept will be at (2.4,0) and y-intercpt ar (0,12).

Step-by-step explanation:

If Joe parked 12 miles away from the cabin and after one hour, he was still 7 miles from the cabin, then he had walked 12 - 7 = 5 miles per hour.

The initial positon of Joe is at point (0,12) (after 0 hours passed, Joe was 12 miles from the cabin). The line must pas through the point (1,7) ( after one hour, he was still 7 miles from the cabin ).

Find the slope:

[tex]\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-12}{1-0}=-5[/tex]

So, the slope of the linear function should be -5 (not -3).

Then the equation of the function is

[tex]f(x)=-5x+12[/tex]

1. Julie’s scenario doesn't match the linear function graphed, because the graphed function is f(x)=-3x+12 and must be f(x)=-5x+12

2. She has counted the slope of the line incorrect.

3. She can write f(x)=-5x+12 and draw the line with the x-intercept will be at (2.4,0) and y-intercpt ar (0,12).