To represent Kyle's budget for video games and music downloads, we will need to define the variables and constraints mathematically.
Let's define:
- Let \( V \) be the number of video games Kyle buys.
- Let \( M \) be the number of music download sessions Kyle purchases.
Each video game costs $25.00, and each music download costs $5.00. Kyle has a total of $100.00 to spend. Therefore, the budget constraint can be represented by the equation:
\[ 25V + 5M \leq 100 \]
We can also simplify this equation by dividing the entire equation by 5:
\[ 5V + M \leq 20 \]
To graph this equation, we need to find the x-intercept and y-intercept:
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Finding the x-intercept (where \( M = 0 \)): \[ 5V + 0 = 20 \implies V = 4 \] So the x-intercept is \( (4, 0) \).
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Finding the y-intercept (where \( V = 0 \)): \[ 5(0) + M = 20 \implies M = 20 \] So the y-intercept is \( (0, 20) \).
The graph will show a line connecting these two intercepts, with the area under and including the line representing the possible combinations of video games and music sessions Kyle can afford. The area above the line would represent combinations that exceed his budget, which are not possible.
When looking at the options (graphs O, P, Q, and R), you would identify the graph that has a line connecting the points (4, 0) and (0, 20) with the shaded area below this line including the axes.
Please take a look at the graphs provided and identify the one that properly represents this situation based on the analysis above.
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