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?

3 miles per minute; it represents the speed of the bird
0.2 mile per minute; it represents the speed of the bird
0.2 mile; it represents the original distance of the bird from its nest
3 miles; it represents the original distance of the bird from its nest

Answer 1

(d).

Explanation:

The y-intercept (0, 3) is initial value of graph ⇒ (d). 3 miles; it represents the original distance of the bird from its nest

Answer 2

`0.2` miles per minute represents the speed of the bird and 3 miles represents the original distance of the bird from its nest.

Explanation:

As there is no graph mentioned here but the information are quite sufficient to answer the question.

We have points
`(0,3), (5,4),(10,5)...`

From these points we can find the slope of the line .

From point slope formula
`y-y_1=m(x-x_1)`

And assigning
`(x,y) (0,3)` and
`(x_1,y_1) (5,4)`

`m=(y_1-y)/(x_1-x) =(4-3)/(5-0) =(1)/(5)=0.2`

This slope is also the speed of the bird which is
`0.2\ miles\ per\ minute.`

As by plugging the values of any coordinate point we can confirm this.

Lets put
`(10,5)`, y-axis is the distance so in
`10` minutes the the distance covered by the bird must be equal to to y-axis value which is
`5` miles.

`y=0.2(x),y=0.2(10)=5\ miles`

Now as in
`t=0` the bird has started from y-intercept value
`3` so we can say that,the original distance of the bird from its nest is
`3\ miles`.

So the correct choices are:
`B` and
`D`

The birds speed is
`0.2\ miles` per minute and is
`3\ miles` away from its nest.