Question

1. write an equation to represent the relationship between the dollar amount kiran is spending and the number of games, x, and the number of rides, y, he could do. 2. which graph represents the relationship between the quantities in this situation? explain how you know. show me work. if you only circle one, you will not get credit

Explanation:

Step1: Determine the cost - relationship equation

Each game costs $0.25 and each ride costs $1. Let the amount of money Kiran is spending be $M$. Then the equation representing the relationship is $M = 0.25x + 1y$, or simply $M=0.25x + y$. Assume Kiran has a fixed amount of money to spend, say $M = 10$ (we can choose any non - negative value for illustration purposes. The general form of the equation for the relationship between $x$ and $y$ when $M$ is fixed is $y=-0.25x + M$). This is a linear equation in the form $y = mx + b$, where $m=-0.25$ (the slope) and $b = M$ (the y - intercept).

Step2: Analyze the slope of the line

The slope $m=-0.25$ means that for every increase of 1 in the number of games $x$, the number of rides $y$ decreases by 0.25. This indicates a negative linear relationship between the number of games and the number of rides.

Step3: Match the graph

Graph A has a positive slope, so it is not correct. Graph B has a very steep negative slope. Graph C has a negative slope with a magnitude of 0.25 (since for an increase of 4 in $x$, $y$ decreases by 1 which is consistent with the slope $m = - 0.25$).

Answer:

1. $M = 0.25x + y$ (where $M$ is the total amount of money Kiran is spending)
2. Graph C. The relationship between the number of games $x$ and the number of rides $y$ is a linear relationship with a negative slope of - 0.25, which is represented by Graph C. As the number of games increases, the number of rides decreases at a rate of 0.25 rides per game.