Laura is driving to Seattle. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes). When graphed, the function gives a line with a slope of -0.75 . See the figure below.Laura has 51 miles remaining after 33 minutes of driving. How many miles were remaining after 15 minutes of driving?

Answer:Laura has 64.5 miles remaining after 15 minutes of driving. Step-by-step explanation:Laura is driving to Seattle. Suppose that the remaining distance to drive (in miles) is a linear function of her driving time (in minutes).Slope of the function = -0.75Laura has 51 miles remaining after 33 minutes of driving.  It means the the line passes through the point (33,51).The point slope form of a line is[tex]y-y_1=m(x-x_1)[/tex]The equation of line is[tex]y-51=-0.75(x-33)[/tex][tex]y-51=-0.75x+24.75[/tex]Add 51 on both sides.[tex]y=-0.75x+24.75+51[/tex][tex]y=-0.75x+75.75[/tex]We need to find how many miles were remaining after 15 minutes of driving.Substitute x=15 in the above equation.[tex]y=-0.75(15)+75.75[/tex][tex]y=64.5[/tex]Therefore, Laura has 64.5 miles remaining after 15 minutes of driving.