Question

Maya is driving to Memphis. 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 -0.7 . See the figure below.

Maya has 59 miles remaining after 30 minutes of driving. How many miles were remaining after 10 minutes of driving

Answer 1

Maya had 73 miles remaining after 10 minutes of driving.

Given that the remaining distance to drive is a linear function of driving time with a slope of -0.7, we can use the point-slope form of a linear equation to represent this situation:

`\[y - y_1 = m(x - x_1)\]`

where:

• y is the remaining distance (in miles),

• x is the driving time (in minutes),

• m is the slope of the line (-0.7), and

• 
  `\((x_1, y_1)\)` is a point on the line.

Using the information provided, we can substitute the values into the equation:

`\[y - 59 = -0.7(x - 30)\]`

Now, we want to find the remaining distance y after 10 minutes of driving x = 10:

`\[y - 59 = -0.7(10 - 30)\]`

Simplify:

`\[y - 59 = -0.7(-20)\]`

`\[y - 59 = 14\]`

Now, solve for y:

`\[y = 14 + 59\]`

`\[y = 73\]`

Therefore, Maya had 73 miles remaining after 10 minutes of driving.