Question

2.4.ps - 14
challenge the value of a baseball player’s rookie card began to increase once the player retired. when he retired, his card was worth $7.48. the value has increased by $2.03 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 2004?
express the relationship with an equation.
y = \square (use integers or decimals for any numbers in the expression.)
enter your answer in the answer box and then click check answer.
2 parts remaining

Explanation:

Step1: Identify the type of relationship

The value of the card starts at $7.48 and increases by $2.03 each year. This is a linear relationship, so the equation will be in the form \( y = mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept (initial value). Here, \( m = 2.03 \) (the annual increase) and \( b = 7.48 \) (the initial value when \( x = 0 \), i.e., when the player retired). So the equation is \( y=2.03x + 7.48 \).

(Note: To find the value in 2004, we would need to know the year when the player retired. Since that information is not fully visible in the problem, but for the equation part, we can derive the linear equation as above.)

Step2: Form the equation

Using the slope - intercept form of a linear equation \( y=mx + b \), with \( m = 2.03 \) and \( b = 7.48 \), we get \( y = 2.03x+7.48 \).

Answer:

\( y = 2.03x + 7.48 \)