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?

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 and , then the equation of line is

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

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

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.