Question

Ashley is driving to Phoenix. 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 -0.85. See the figure below.Ashley has 49 miles remaining after 38 minutes of driving. How many miles were remaining after 22 minutes of driving?

Answer 1

The given graph gives a linear relationship between the driving time 'x' and the remaining distance 'y'.

Since the relationship is linear with slope -0.85, its equation is given by,

`y=-0.85x+c`

Here 'c' is the y-intercept.

At x=38, the value is y=49,

`\begin{gathered} 49=-0.85(38)+c \\ 49=-32.3+c \\ c=49+32.3 \\ c=81.3 \end{gathered}`

Substitute the value in the equation,

`y=-0.85x+81.3`

Now, solve for 'y' when the value of 'x' is 22,

`\begin{gathered} y=-0.85(22)+81.3 \\ y=-18.7+81.3 \\ y=62.6 \end{gathered}`

Thus, 62.6 miles were remaining after 22 minutes of driving.