Answer:
(a) [tex]y = 4.5x + 22[/tex] -- The equation
(b) 31 inches
Step-by-step explanation:
Given
See attachment
Solving (a): The equation of the trend line.
We start by calculating the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where
[tex](x_1,y_1) = (0,22)[/tex]
[tex](x_2,y_2) = (4,40)[/tex]
So, we have:
[tex]m = \frac{40 - 22}{4 - 0}[/tex]
[tex]m = \frac{18}{4}[/tex]
[tex]m = 4.5[/tex]
The equation is then calculated using:
[tex]y = m(x-x_1)+y_1[/tex]
Where:
[tex](x_1,y_1) = (0,22)[/tex]
[tex]m = 4.5[/tex]
[tex]y = 4.5(x - 0) + 22[/tex]
Open bracket
[tex]y = 4.5x - 0 + 22[/tex]
[tex]y = 4.5x + 22[/tex]
(b) The height of a 2 year old.
To do this, we substitute 2 for x in [tex]y = 4.5x + 22[/tex]
[tex]y = 4.5 * 2 + 22[/tex]
[tex]y = 9+ 22[/tex]
[tex]y = 31[/tex]
The prediction is 31 inches
