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?

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:

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

Then the equation of the function is

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).

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is