Question

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

Part A
Drag numbers to complete an equation for the trend line. Numbers may be used once, more than once, or not at all.

(22, 2.5, 18, 32, 4.5)

y = ?x + ?

Part B
Using the linear equation, predict the average height for a two-year old.

A. 15 inches
B. 22 inches
C. 31 inches
D. 35 inches​

Answer 1

(a)
`y = 4.5x + 22` -- The equation

(b) 31 inches

Explanation:

Given

See attachment

Solving (a): The equation of the trend line.

We start by calculating the slope (m)

`m = (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 = (40 - 22)/(4 - 0)`

`m = (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