The graph shows the distance traveled by a train over x hours. Which of the inequalities shows when the train has traveled at least 400 miles?

A graph is shown in the xy-plane. The values on the x-axis ranges from 0 to 16 in increments of 2 and the values on the y-axis ranges from 0 to 900 in increments of 100. A line starts from the origin, goes up and passes through the point (5, 400).
A. x≥400

B. x≥5

C. x>400

D. x>5

The correct answer is option D.

According to the graph, the train starts at the origin (0,0) and travels up the line passing through (5,400). This means that after 5 hours, the train has traveled at least 400 miles. Therefore, the inequality should be x>5 to represent the time during which the train has traveled at least 400 miles.

To determine the inequality that represents when the train has traveled at least 400 miles, we need to find the x-value when the y-value is at least 400.

Looking at the graph, we can see that the line starts from the origin (0,0) and passes through the point (5,400). This means that when x=5, the train has traveled 400 miles.

Since we want to find when the train has traveled at least 400 miles, we need to consider values of x that are greater than or equal to 5.

Therefore, the correct inequality is:

B. x≥5

To determine which inequality represents when the train has traveled at least 400 miles, we need to analyze the graph.

First, identify the point where the line on the graph crosses the y-axis at y = 400. This point represents the distance traveled after x hours.

From the graph, we can see that the line passes through the point (5, 400). This means that after 5 hours, the train has traveled 400 miles.

Now, let's consider the options provided:

A. x ≥ 400: This inequality states that x is greater than or equal to 400. However, in the context of the graph, it does not accurately represent the time it takes for the train to travel at least 400 miles.

B. x ≥ 5: This inequality states that x is greater than or equal to 5. Since the line passes through the point (5, 400), this option accurately represents when the train has traveled at least 400 miles. This is the correct answer.

C. x > 400: This inequality states that x is strictly greater than 400. However, our graph does not extend beyond 16 on the x-axis, so this option is not relevant.

D. x > 5: This inequality states that x is strictly greater than 5. Since the line passes through the point (5, 400), this option accurately represents when the train has traveled at least 400 miles. However, it is not as inclusive as option B, which includes the case when exactly 5 hours have passed.

In conclusion, the correct inequality is B. x ≥ 5.