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?

Accepted Solution

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 problemLetx -----> the time in hoursy ----> the distance in miles from the cabinwe know thatAfter one hour, he was still 7 miles from the cabin.soFor x=1 h, y=7 miObserving the graph For x=1 h, y=9 mithereforeJulie's scenario does not match the graphed linear function.Find the correct linear equation that match Julie’s scenariowe 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]thereforeThe linear function that matches Julie's scenario is[tex]y=-5x+12[/tex]