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After 3 months of living at her new apartment, Renae had 1 dog. Eight months later, Renae still had 1 dog. Which of the graphs below models Renae's dog population? graph of line going through 1, 0 and 1, 8 graph of line going through 1, 2 and 3, 4 graph of line going through 2, 1 and 4, 3 graph of line going through 0, 1 and 7, 1

Respuesta :

The graph would need to go through the coordinates (0, 1) and (8, 1) instead of (1, 0) and (1, 8); we would plot the population on the y (dependent) axis and time on the x (independent) axis.

Answer:

The graph of line is going through (0, 1) and (7, 1).

Step-by-step explanation:

Let x-axis denote the Number of months.

and y-axis denote the number of dogs.

It is given that:

  • After 3 months of living at her new apartment, Renae had 1 dog i.e. the point on the graph is: (3,1).
  • Eight months later, Renae still had 1 dog i.e. point on the graph is: (8,1).

Now we are asked to find that the line formed by the above information passes through which point.

so, for finding this firstly we need to find the equation of the line with the help of the two points:

(3,1) and (8,1).

We know that the equation of line passing through two points (a,b) and (c,d) is given as:

[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]

Here (a,b)=(3,1)  and (b,d)=(8,1)

Hence, equation of line is:

[tex]y-1=\dfrac{1-1}{8-3}\times (x-3)\\\\y-1=0\times (x-3)\\\\y-1=0\\\\y=1[/tex]

Hence, the line is a straight line parallel to x-axis.

i.e. the graph will pass through the point (x,1) for any 'x'.

So, the option that holds true is:

graph of line going through (0, 1) and (7, 1)

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