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

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

Step-by-step explanation:

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

We have points

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

From point slope formula

And assigning and

This slope is also the speed of the bird which is

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

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

Now as in the bird has started from y-intercept value so we can say that,the original distance of the bird from its nest is .

So the correct choices are: and

The birds speed is per minute and is away from its nest.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!