Question

Trey is driving to New York City. Suppose that the remaining distance to drive (in miles) is a linear function of his driving time (in minutes). When graphed, the

function gives a line with a slope of -0.7. See the figure below.
Trey has 48 miles remaining after 31 minutes of driving. How many miles were remaining after 17 minutes of driving?
Remaining
distance
(in miles)
48
Driving time
(in minutes)
miles

Answer 1

Answer 57.8


To determine the number of miles remaining after 17 minutes of driving, we can use the information given about the linear function and the data point provided.

We are told that the linear function has a slope of -0.7. The slope represents the rate at which the distance changes with respect to time. In this case, it means that for every minute Trey drives, the distance remaining decreases by 0.7 miles.

We are also given a data point: after 31 minutes of driving, there are 48 miles remaining. This data point can be represented as (31, 48), where 31 is the driving time in minutes and 48 is the remaining distance in miles.

Using this information, we can set up an equation to represent the linear function. The equation for a linear function is y = mx + b, where y represents the dependent variable (remaining distance), x represents the independent variable (driving time), m represents the slope, and b represents the y-intercept.

In this case, we know that m = -0.7 and we need to find b. To find b, we can substitute the values from the given data point into the equation:

48 = -0.7 * 31 + b

Simplifying this equation gives us:

48 = -21.7 + b

To isolate b, we add 21.7 to both sides of the equation:

b = 48 + 21.7
b = 69.7

Now that we have determined b, we can use it to find the remaining distance after 17 minutes of driving. We substitute x = 17 into the equation:

y = -0.7 * 17 + 69.7

Simplifying this equation gives us:

y = -11.9 + 69.7
y = 57.8

Therefore, after 17 minutes of driving, there were 57.8 miles remaining.

In summary, after 17 minutes of driving, there were approximately 57.8 miles remaining.

Answer 2

To find the remaining distance after 17 minutes of driving, we can use the slope-intercept form of a linear equation: y = mx + b, where y is the remaining distance, x is the driving time, m is the slope, and b is the y-intercept.

From the given information, we know that the slope of the line is -0.7. Let's call the remaining distance after 17 minutes y1. We can set up the following equation:

y1 = -0.7 * 17 + b

To find b, we can use the fact that Trey had 48 miles remaining after 31 minutes of driving. Let's call the remaining distance after 31 minutes y2. We can set up the following equation:

y2 = -0.7 * 31 + b

Substituting the values for y2 and x2 into the equation, we get:

48 = -0.7 * 31 + b

Now we can solve for b:

b = 48 + 0.7 * 31

b = 48 + 21.7

b = 69.7

Finally, we can substitute the value of b into the equation for y1:

y1 = -0. 7 * 17 + 69.7

y1 = -11.9 + 69.7

y1 = 57.8

Therefore, after 17 minutes of driving, there were 57.8 miles remaining.