Answer:
The correct option is C.
Step-by-step explanation:
The graph below shows a scatter plot and the line of best fit relating the ages of children and the total number of times they have visited the doctor.
If a line passes through two points then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
From the given graph it is clear that the line of best fit passes through the points (0,0) and (3,10). So, the equation of best fit line is
[tex]y-0=\frac{10-0}{3-0}(x-0)[/tex]
[tex]y=\frac{10}{3}x[/tex] .... (1)
The equation of best fit line is [tex]y=\frac{10}{3}x[/tex]. Where, x is age in year and y shows the total number of visits to the doctor.
We need to estimate the age of a child who has visited the doctor 40 times.
Substitute y=40 in equation (1), to find the value of x.
[tex]40=\frac{10}{3}x[/tex]
Multiply both sides by 3.
[tex]120=10x[/tex]
Divide both sides by 10.
[tex]12=x[/tex]
The value of x is 12. It means the age of a child who has visited the doctor 40 times is 12.
Therefore the correct option is C.
