The graph shows the distance traveled by a dirt bike and a car in miles, y. as a function of time in
minutes, z.
Complete the statement.
The rate of change of the dirt bike is
the rate of change
less than
of the car.
The dirt bike is moving
slower than
the car.
Distance (mi)
Dirt Bike
Car
0
0
0
2
4
6
8
10
12
14
Time (min)
2
4
6
8
10
12
14
To determine the rate of change of the dirt bike and the car from the graph, we need to find the slope of each line. The slope represents the rate of change of distance with respect to time.
To find the slope, we can choose any two points on each line and calculate the change in distance divided by the change in time (i.e., rise over run).
Let's say we choose two points for the dirt bike line: (time1, distance1) and (time2, distance2). Similarly, for the car line, let's choose two points: (time3, distance3) and (time4, distance4) from the graph.
Now, we have the following information:
- For the dirt bike:
Slope of dirt bike line = (distance2 - distance1) / (time2 - time1)
- For the car:
Slope of car line = (distance4 - distance3) / (time4 - time3)
To compare the rates of change, we can directly compare the slopes of the two lines. If the slope of the dirt bike line is less than the slope of the car line, then the rate of change of the dirt bike is less than the rate of change of the car.
So, completing the statement:
"The rate of change of the dirt bike is less than the rate of change of the car."
or in simpler terms:
"The dirt bike is moving slower than the car."
To complete the statement, we need to analyze the graph and compare the rate of change of the dirt bike and the car.
Looking at the graph, we can observe that the slope (steepness) of the dirt bike's line is less than the slope of the car's line. This indicates that the rate of change of the dirt bike is less than the rate of change of the car.
Therefore, we can conclude that the rate of change of the dirt bike is less than the rate of change of the car. In other words, the dirt bike is moving slower than the car.