Final answer:
The value of the baseball player's rookie card and the number of years since his retirement can be expressed by the equation Y = 2.07X + 5.91. This equation is linear but not directly proportional due to a non-zero y-intercept. The value of the card in 2008, equating to 8 years of retirement, is $22.55.
Step-by-step explanation:
A linear equation is a mathematical expression of the form ax+b=0ax+b=0, where xx is the variable, and aa and bb are constants. The solution, obtained by isolating xx, represents a point on a line when graphed and holds a linear relationship between variables in algebraic contexts.
The value of the baseball player's rookie card and the number of years since retirement can be expressed as a linear equation. If we know that the initial value of the card was $5.91 when the player retired in 2000, and that the value has increased by $2.07 each year since then, the equation that models this relationship is Y = 2.07X + 5.91, where Y is the value of the card in dollars, and X is the number of years the player has been retired.
This relationship between X and Y is linear, but it is not directly proportional, as there is a non-zero y-intercept (i.e., the initial value of the card when X=0). To find the value of the card in 2008, we need to calculate the number of years of retirement as of 2008, which is 2008 - 2000 = 8 years. Substituting X = 8 into the equation gives us Y = 2.07(8) + 5.91, resulting in Y = $22.55.