The value of a baseball player's rookie card began to increase once the player retired. When he retired in 1996 1996 his card was worth $ 8.76 8.76. The value has increased by $ 1.92 1.92 each year since then. Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in 2006 2006?

Part 1) Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation

Let

x -----> the number of years since 1996

y ----> the value of the card

we know that

The linear equation in slope intercept form is

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-coordinate of the y-intercept

In this problem

we have that

1) The value of the card has increased by $ 1.92 each year since 1996

so

The unit rate or slope of the linear equation is [tex]m=1.92\frac{\$}{year}[/tex]

2) When he retired in 1996 his card was worth $ 8.76

Remember that the y-intercept is the value of y when the value of x is equal to zero

In this problem, the y-intercept is the value of the card when the year is 1996 (the number of years is zero)

so

The y-intercept is the point (0,8.76)

[tex]b=\$8.76[/tex]

substitute the values in the linear equation

[tex]y=1.92x+8.76[/tex]

This relation is not proportional, because the linear equation not passes trough the origin

Part 2) What was the value of the card in 2006?

Determine the number of years since 1996

x=2006-1996=10 years

substitute the value of x in the equation and solve for y

[tex]y=1.92(10)+8.76[/tex]

[tex]y=\$27.96[/tex]