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

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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taater taater · Answer 1 · 2019-10-01T14:45:03+02:00

Answer:

The graph that Julie drew is wrong, I don't know where she went wrong but the graph should look like this: (image shown below)

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erinna erinna · Answer 2 · 2019-10-17T09:34:57+02:00

Answer:

Yes, she made a mistake in the statement "after one hour, Joe was still 7 miles from the cabin". She should write 9 instead of 7 in that statement.

Step-by-step explanation:

If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The given graph passes through the point (0,12) and (4,0). So, the equation of line is

[tex]y-12=\frac{0-12}{4-0}(x-0)[/tex]

[tex]y-12=-3x[/tex]

[tex]y=-3x+12[/tex]

Therefore the graph represented by the equation y=-3x+12.

The initial value of the function is 12. The value of function after one unit is

[tex]y=-3(1)+12=9[/tex]

In her scenario she write that after one hour, joe was still 7 miles from the cabin.

7 ≠ 9

So, she made a mistake in her scenario. She should write 9 instead of 7 in her scenario.