Question

Rita is driving to San Francisco. 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. Rita has 45 miles remaining after 36 minutes of driving. How many miles will be remaining after 48 minutes of driving?

Answer 1

GIVEN:

We are given a graph that shows the relationship between the driving time and the remaining distance after driving a given number of minutes. The slope of the line represnting this relationship is given as -0.75.

Also, after driving for 36 minutes, Rita has 45 miles remaining.

Required;

To determine how many miles will be remaining after 48 minutes of driving.

Step-by-step solution;

What we have is a linear relationship such that as one variable increases, the other decreases. We know this because the slope of the line is a negative one, moving downwards from left to right.

The slope-intercept form of an equation is given as follows;

`y=mx+b`

The variables x and y can be determined from the graph as;

`(x,y)=(36,45)`

The slope m, is given as;

`m=-0.75`

Now we can substitute these into the equation in slope-intercept form;

`\begin{gathered} y=mx+b \\ \\ 45=-0.75(36)+b \\ \\ 45=-27+b \\ \\ Add\text{ }27\text{ }to\text{ }both\text{ }sides: \\ \\ 72=b \end{gathered}`

Now we can derive an equation for the relationship between time driven and miles remaining;

We substitute the values of m and b into the equation quoted earlier;

`\begin{gathered} y=mx+b \\ \\ \rightarrow y=-0.75x+72 \end{gathered}`

Next, we want to determine how many miles will be remaining after 48 minutes of driving. In other words, we have the value of x, and we want to determine the corresponding value of y.

We now have,

`\begin{gathered} y=-0.75x+72 \\ \\ y=-0.75(48)+72 \\ \\ y=-36+72 \\ \\ y=36 \end{gathered}`

ANSWER:

After 48 minutes of driving, there will be 36 miles remaining.