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. Laura has 51 miles remaining after 33 minutes of driving. How many miles were remaining after 15 minutes of driving?
15
18
To find the number of miles remaining after 15 minutes of driving, we can use the information given about the linear function's slope and a point on the line.
First, let's call the number of miles remaining after x minutes as y. Since the function graphed is a linear function, it can be represented by the equation y = mx + b, where m is the slope of the line, x is the driving time in minutes, and b is the y-intercept.
In this case, we are given that the slope of the line is -0.75, so our equation becomes y = -0.75x + b.
We are also given a point on the line: after 33 minutes of driving, Laura has 51 miles remaining. Therefore, we can substitute x = 33 and y = 51 into the equation to find the value of b.
51 = -0.75(33) + b
51 = -24.75 + b
b = 75.75
Now, we have the equation for the linear function: y = -0.75x + 75.75.
To find the number of miles remaining after 15 minutes of driving, we can substitute x = 15 into the equation:
y = -0.75(15) + 75.75
y = -11.25 + 75.75
y = 64.5
Therefore, after 15 minutes of driving, Laura had 64.5 miles remaining.