Subjects algebra

Inverse Proportion 6Fc355

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1. **Stating the problem:** We have an inverse proportional relationship between the number of friends $x$ and the money $y$ given by the equation $$y = \frac{480}{x}.$$ We want to find how much the money changes (goes up or down) as the number of friends changes on the graph. 2. **Understanding inverse proportionality:** In an inverse proportional relationship, as $x$ increases, $y$ decreases, and vice versa. The product $xy$ is constant: $$xy = 480.$$ This means if you increase the number of friends, the money per friend decreases. 3. **Calculating the change in money:** To find how much the money changes when the number of friends changes, calculate the difference in $y$ values for consecutive $x$ values. For example, from 2 friends to 3 friends: $$y_2 = \frac{480}{2} = 240,$$ $$y_3 = \frac{480}{3} = 160,$$ Change in money: $$\Delta y = y_3 - y_2 = 160 - 240 = -80.$$ The money decreases by 80. From 3 friends to 4 friends: $$y_3 = 160,$$ $$y_4 = \frac{480}{4} = 120,$$ Change in money: $$\Delta y = 120 - 160 = -40.$$ The money decreases by 40. 4. **Summary:** The money does not go up as the number of friends increases; it goes down. The amount it decreases by gets smaller as the number of friends increases. **Final answer:** The money decreases by $80$ when going from 2 to 3 friends, and by $40$ when going from 3 to 4 friends, showing the inverse proportional relationship on the graph.