Question

The graph shows the distance y, in miles, of a moving train from a station over a certain period of time, x, in hours:

A graph titled Distance Vs Time is shown with Time in hours labeled on x-axis and Distance from Station in miles labeled on y-axis. The scale on the x-axis shows the numbers 1, 2, 3, 4, 5, 6, 7, and the scale on the y-axis shows the numbers 0, 45, 90, 135, 180, 225, 270, 315, 360. The graph shows a straight line joining the ordered pairs 0, 90, and 1, 135, and 2, 180, and 3, 225, and 4,270.

What is the speed (in miles per hour) of the train and why?

45 miles per hour, because speed is the rate of change of distance
90 miles per hour, because speed is the initial value of the function
135 miles per hour, because speed is the distance traveled in unit time
270 miles per hour, because speed is the distance traveled in a certain time

@prestonrobotics

Answer 1

It is the first answer, 45. To find the answer you find the rate of change by dividing the input  (x) and output (y). On the graph the y coordinates the distance increases by 45, and on the x coordinate the hours increase by one.

Answer 2

Answer:

45 miles per hour, because speed is the rate of change of distance

Step-by-step explanation:

Speed is a rate of change.  It indicates how much the distance changes per unit of time.

In this situation, the train goes from (0, 90) to (1, 135).  This shows us that the distance changed by 135-90 = 45 miles over 1-0 = 1 hour.  This gives us the speed 45 miles per hour.