Question

The graph below shows the distance, y, in feet, of a mouse from its hole, for a certain amount of time, x, in minutes:

Graph titled Distance Vs Time is shown with Time in minutes along the x-axis and Distance from Hole in miles along the y-axis. The scale on the x-axis shows the numbers 0 to 45 at increments of 9, and the scale on the y-axis shows the numbers 3 to 24 at increments of 3. A straight line joins the ordered pairs 0, 9 and 9, 12 and 18, 15 and 27, 18 and 36, 21.


Based on the graph, what is the initial value of the graph and what does it represent?


a: 0.23 foot per minute; it represents the speed of the mouse

b: 9 feet; it represents the original distance of the mouse from its hole

c: 0.23 foot; it represents the original distance of the mouse from its hole

d: 9 feet per minute; it represents the speed of the mouse

Answer 1

the correct answer is;
9 feet because it represents the original distance of the mouse from its hole

Answer 2

We have that the initial value of the function is the value at x=0; this is equal to 9. It shows the initial distance from the hole, when no time has passed (x=0). This is so because y has the units of distance. THe slope of the line is the quantity that shows the rate of change, namely how much a change in x is converted to a change in y. This is so because the slope has the units of y/x, namely distance over time (so it shows speed). Correct is b.