Question

the graph shows the relationship between the number of hours that michelle has been driving and the distance that she has left to travel to get to her destination.
distance remaining over time
which statement is true?
it took michelle 6 hours to complete the trip.
for each hour that michelle drove, she traveled an additional 50 miles.
in the first 6 hours, michelle had traveled a total of 50 miles.
in the first 3 hours, michelle had traveled a total of 200 miles.

Explanation:

Step1: Analyze the graph's intercepts

The y - intercept is at (0, 350), meaning at time \(x = 0\) (start of the trip), the distance to the destination is 350 miles. The x - intercept is at (7, 0), meaning the trip is completed in 7 hours. So the first option "It took Michelle 6 hours to complete the trip" is false.

Step2: Calculate the slope (rate of change)

The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using points (0, 350) and (7, 0), \(m=\frac{0 - 350}{7 - 0}=\frac{- 350}{7}=- 50\). The negative sign indicates a decrease in distance remaining per hour. So the rate of travel (speed) is 50 miles per hour. This means for each hour she drives, she travels an additional 50 miles. Let's check other options.

Step3: Check the third option

In the first 6 hours, the distance remaining \(y\) when \(x = 6\): using the equation of the line \(y=-50x + 350\) (from slope - intercept form \(y=mx + b\), where \(m=-50\) and \(b = 350\)). When \(x = 6\), \(y=-50\times6+350=-300 + 350 = 50\) miles. So the distance traveled is \(350 - 50=300\) miles, not 50 miles. So the third option is false.

Step4: Check the fourth option

In the first 3 hours, using \(y=-50x + 350\), when \(x = 3\), \(y=-50\times3+350=-150 + 350 = 200\) miles. So the distance traveled is \(350 - 200 = 150\) miles, not 200 miles. So the fourth option is false.

Answer:

For each hour that Michelle drove, she traveled an additional 50 miles.