Question

cost of raising a child born in 2013
childs age 2 5 8 11 14
annual cost ($) 12,940 12,970 12,800 13,600 14,420
make a scatter plot on a separate sheet of paper and describe what relationship exists within the data.
there is select choice correlation between the childs age and annual cost.
part b
use the points (8, 12,800) and (14, 14,420) to enter and interpret the equation of the line of fit in slope - intercept form.
y = x+
the cost of raising a child increases $ each year. the cost of raising a child from birth to age 1 is $

Explanation:

Step1: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(8,12800)\) and \((x_2,y_2)=(14,14420)\).

$$m=\frac{14420 - 12800}{14 - 8}=\frac{1620}{6}=270$$

Step2: Find the \(y -\)intercept \(b\)

Use the point - slope form \(y - y_1=m(x - x_1)\). Substitute \(m = 270\), \(x_1=8\) and \(y_1 = 12800\)

$$y-12800=270(x - 8)$$

$$y-12800=270x-2160$$

$$y=270x+(12800 - 2160)$$

$$y=270x + 10640$$

Answer:

\(y = 270x+10640\); The cost of raising a child increases \(\$270\) each year. The cost of raising a child from birth to age 1 is \(\$10640\) (assuming \(x = 0\) represents birth, and we use the \(y -\)intercept of the line of fit as an estimate for the cost at \(x = 0\) (birth - to - age - 1, since the model is a linear approximation)).