Question

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.

Use the line of best fit to estimate the age of a child who has visited the doctor 40 times.

A. 14 years old
B. 13 years old
C. 12 years old
D. 11 years old

Answer 1

The kid is around 12 years old that visits the doctor 40 times

Answer 2

The correct option is C.

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

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

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

`y-0=(10-0)/(3-0)(x-0)`

`y=(10)/(3)x` .... (1)

The equation of best fit line is
`y=(10)/(3)x`. 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.

`40=(10)/(3)x`

Multiply both sides by 3.

`120=10x`

Divide both sides by 10.

`12=x`

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.