To determine which graph represents the number of pizzas and sodas Sarah can purchase with her $40.00 budget, we can set up an equation based on the prices of pizzas and sodas.
Let:
- \( p \) = number of pizzas
- \( s \) = number of sodas
The cost of pizzas and sodas together must not exceed her budget of $40.00. Given:
- Each pizza costs $8.00
- Each soda costs $2.00
The total cost can be expressed as: \[ 8p + 2s \leq 40 \]
To analyze what this inequality means, we can rearrange it: \[ 2s \leq 40 - 8p \] \[ s \leq 20 - 4p \]
This equation (standard linear form) provides a boundary line on a graph where:
- The y-axis (s) represents the number of sodas.
- The x-axis (p) represents the number of pizzas.
The graph will be a straight line with a slope of -4, with the y-intercept at \( s = 20 \) (when no pizzas are purchased) and crossing the x-axis at \( p = 5 \) (when no sodas are purchased). The area below this line (including the line itself) will represent all the combinations of pizzas and sodas that can be bought under the budget.
To verify:
- If \( p = 0 \) (0 pizzas), then \( s \) can be 20 (20 sodas).
- If \( p = 5 \) (5 pizzas), then \( s \) can be 0 (0 sodas).
- For \( p = 1 \) (1 pizza, costs $8), the remaining budget is $32, allowing for \( s = 16 \) (16 sodas).
You would select the graph that features a line with a slope of -4 intersecting the y-axis at 20 and the x-axis at 5, with the area below it filled in, indicating the feasible solutions for soda and pizza combinations that don't exceed the budget.
Without viewing the actual graphs (W, X, Y, or Z), I suggest looking for the characteristics described above to determine the correct representation.