After crossing a bridge, Trey drives at a constant speed. The graph below shows the distance (in miles) versus the time since Trey crossed the bridge (in hours).
Use the graph to answer the questions.
Distance (miles)
y50100150200250300350400x12345670
Time (hours)
(a) What is the distance traveled at 0 hours?
(b) What is the distance traveled at 1 hour?
(c) How much does the distance increase for each hour since Trey crossed the bridge?
(d) Are the amounts given in parts (b) and (c) equal?
Why or why not? Choose the best answer.
Yes, because the line passes through 0,0.
Yes, because the line does not pass through 0,0.
No, because the line passes through 0,0.
No, because the line does not pass through 0,0.
(a) The distance traveled at 0 hours is 0 miles.
(b) The distance traveled at 1 hour is 100 miles.
(c) The distance increases by 100 miles for each hour since Trey crossed the bridge.
(d) No, the amounts given in (b) and (c) are not equal. The amount in (b) represents the total distance traveled in a specific time (1 hour), while the amount in (c) represents the increase in distance for each hour since Trey crossed the bridge.
(a) The distance traveled at 0 hours is 0 miles.
(b) The distance traveled at 1 hour is 50 miles.
(c) The distance increases by 50 miles for each hour since Trey crossed the bridge.
(d) The amounts given in parts (b) and (c) are equal. No, because the line passes through 0,0.
To answer these questions, we need to analyze the graph provided. The graph shows the distance (in miles) on the y-axis and the time since Trey crossed the bridge (in hours) on the x-axis.
(a) To find the distance traveled at 0 hours, we need to determine the y-coordinate when x=0 on the graph. Looking at the graph, we can see that the line intersects the y-axis at a point above 0. However, the exact value is not given in the graph. Therefore, without more information, we are unable to determine the distance traveled at 0 hours.
(b) To find the distance traveled at 1 hour, we need to determine the y-coordinate when x=1 on the graph. Looking at the graph, we can see that when x=1, the line intersects the y-axis at the point 100. Therefore, the distance traveled at 1 hour is 100 miles.
(c) To determine how much the distance increases for each hour since Trey crossed the bridge, we need to calculate the slope of the line. In this case, the slope is equal to the change in distance divided by the change in time. Looking at the graph, we can observe that for every 1 hour increase in time, the distance increases by 100 miles (from 100 to 200, 200 to 300, etc.). Therefore, the distance increases by 100 miles for each hour since Trey crossed the bridge.
(d) By comparing the distance traveled at 1 hour (100 miles) and the amount by which the distance increases for each hour (100 miles), we can see that they are equal. This is because the line passes through the point (0,0) on the graph, indicating that the distance traveled at 0 hours is zero. Therefore, the answer is: Yes, the amounts given in parts (b) and (c) are equal because the line passes through 0,0.