Question

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​?

Answer 1

Answer:

Part 1) The equation is $y=1.92x+8.76$

Part 2) The value of the card in 2006  was $\ 27.96$

Step-by-step explanation:

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

$y=mx+b$

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 $m=1.92\frac{\ }{year}$

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)

$b=\ 8.76$

substitute the values in the linear equation

$y=1.92x+8.76$

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

$y=1.92(10)+8.76$

$y=\ 27.96$