Respuesta :
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 = -0.75
Laura 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.
