A bowling alley charges 14 for the first game, 10 for the second game, and 5 per game for every game after that. Which statement is true based on the given description? (2 points) The description shows a linear relationship and a proportional relationship. The description does not show a linear relationship or a proportiona relationship. The description shows a proportional relationship but not a linear relationship. The description shows a linear relationship, but not a proportional relationship.

To determine whether the relationship described in the problem is linear or proportional, we need to analyze the cost of each game.<br /><br />Given information:<br />- The bowling alley charges $14 for the first game.<br />- The bowling alley charges $10 for the second game.<br />- The bowling alley charges $5 for each game after that.<br /><br />Let's define the variables:<br />- Let x be the number of games played.<br /><br />The cost of each game can be represented as:<br />- Game 1: $14<br />- Game 2: $10<br />- Game 3 and beyond: $5 per game<br /><br />The total cost, C, can be calculated as:<br />C = $14 + $10 + $5(x - 2)<br /><br />Simplifying the equation:<br />C = $24 + $5(x - 2)<br />C = $24 + $5x - $10<br />C = $5x + $14<br /><br />The equation C = $5x + $14 is a linear equation, as it has the form y = mx + b, where m is the slope and b is the y-intercept.<br /><br />However, this relationship is not proportional because the cost is not directly proportional to the number of games played. The cost is not a constant multiple of the number of games, as there is a fixed cost of $24 for the first two games.<br /><br />Therefore, the correct statement is:<br />The description shows a linear relationship, but not a proportional relationship.