1. **Problem Statement:** Elyza has 12 units of money to spend on popsicles and ice cream sandwiches. The graph shows the trade-off between the number of popsicles (y-axis) and ice cream sandwiches (x-axis) she can buy. 2. **Understanding the Graph:** The line from (0,12) to (6,0) represents all combinations where the total cost equals 12. This line can be expressed as a linear equation. 3. **Finding the Equation of the Line:** The line passes through points (0,12) and (6,0). The slope $m$ is calculated as: $$m = \frac{0 - 12}{6 - 0} = \frac{-12}{6} = -2$$ Using point-slope form with point (0,12): $$y - 12 = -2(x - 0)$$ Simplifies to: $$y = -2x + 12$$ 4. **Interpreting the Equation:** This means for every ice cream sandwich bought (increase in $x$ by 1), the number of popsicles decreases by 2 to keep the total cost at 12. 5. **Checking the Given Equations:** Among the options: - $2x - y = 12$ rearranges to $y = 2x - 12$ (incorrect slope) - $x + 2y = 12$ rearranges to $y = \frac{12 - x}{2}$ (incorrect slope) - $2x + y = 12$ rearranges to $y = 12 - 2x$ (matches our equation) - $2x + y = 6$ rearranges to $y = 6 - 2x$ (incorrect intercept) 6. **Conclusion:** The correct equation representing the graph is: $$2x + y = 12$$ 7. **About the Quadrilateral:** The vertices (4,0), (6,4), (2,6), (0,2) form an irregular quadrilateral, possibly representing feasible purchase combinations under different constraints. **Final answer:** The equation of the line is $$2x + y = 12$$ which matches the graph of Elyza's snack options.