Question

The scatter plot shows the average heights of children up to age 5.

Answer 1

Answer:

(a) $y = 4.5x + 22$ -- 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)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where

$(x_1,y_1) = (0,22)$

$(x_2,y_2) = (4,40)$

So, we have:

$m = \frac{40 - 22}{4 - 0}$

$m = \frac{18}{4}$

$m = 4.5$

The equation is then calculated using:

$y = m(x-x_1)+y_1$

Where:

$(x_1,y_1) = (0,22)$

$m = 4.5$

$y = 4.5(x - 0) + 22$

Open bracket

$y = 4.5x - 0 + 22$

$y = 4.5x + 22$

(b) The height of a 2 year old.

To do this, we substitute 2 for x in $y = 4.5x + 22$

$y = 4.5 * 2 + 22$

$y = 9+ 22$

$y = 31$

The prediction is 31 inches