Question

The graph below shows the distance, y, in miles, of a bird from its nest 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 Nest in miles along the y-axis. The scale on the x-axis shows the numbers 0 to 25 at increments of 5, and the scale on the y-axis shows the numbers 1 to 8 at increments of 1. A straight line joins the ordered pairs 0, 3 and 5, 4 and 10, 5 and 15, 6 and 20, 7. Based on the graph, what is the initial value of the graph and what does it represent?

Answer 1

The initial value of graph is: (0,3)

Explanation:

The graph of this situation is a straight line that passes through the points:

(0,3) , (5,4) , (10,5) , (15,6) and (20,7)

Where the first ordinate displays the time in minutes and the second values denotes the distance of the bird from the nest in miles.

Time(in minutes) Distance (in miles)

0 3

5 4

10 5

15 6

20 7

The initial value of the graph is: (0,3).

It represents the initial distance of the bird from the nest initially i.e. before any elapsed time i.e. the time before the readings were taken or the starting time.

The bird was initially at 3 miles from the nest.

Answer 2

The initial value is 3

It represents the distance between the bird and its nest before any elapsed time which is 3 miles.

Explanation:

The graph is shown in the attached image.

The general form of a straight line is:

y = mx + c

where:

m is the slope and c is the y-intercept.

The y-intercept is also known as the initial value. It is the value of y at x=0.

From the givens, we can note that at x = 0, the y-value is 3. This means that the y-intercept is 3.

Now, in the problem, x represents the time in minutes while y represents the distance of the bird from the nest in miles.

At x = 0, meaning before any time elapsed, the distance of the bird from its nest was 3 miles.

Hope this helps :)