1. **State the problem:** The Fabulous Fish Market buys tilapia at 3 per pound and salmon at 5 per pound, with a daily budget of 210. 2. **Define variables and write the equation:** Let $x$ = pounds of tilapia and $y$ = pounds of salmon. The total cost equation is: $$3x + 5y = 210$$ 3. **Check given combinations:** We verify if each pair $(x,y)$ satisfies $3x + 5y = 210$. - For (5, 36): $3(5) + 5(36) = 15 + 180 = 195 \neq 210$ - For (27, 25): $3(27) + 5(25) = 81 + 125 = 206 \neq 210$ - For (65, 16): $3(65) + 5(16) = 195 + 80 = 275 \neq 210$ - For (19, 30): $3(19) + 5(30) = 57 + 150 = 207 \neq 210$ - For (25, 27): $3(25) + 5(27) = 75 + 135 = 210$ ✓ Only (25, 27) satisfies the budget exactly. 4. **Rewrite the equation to express $y$ in terms of $x$ for graphing:** $$3x + 5y = 210$$ $$5y = 210 - 3x$$ $$y = \frac{210 - 3x}{5}$$ 5. **Explain the graph:** - $x$-axis: pounds of tilapia - $y$-axis: pounds of salmon - The line represents all combinations of $x$ and $y$ that cost exactly 210. 6. **Plot points A-F on the graph:** Given points: - A = (5, 36) - B = (19, 30.6) - C = (27, 25) - D = (25, 27) - E = (65, 6) - F = (55, 4) Check if these points lie on the line: - For A: $3(5) + 5(36) = 15 + 180 = 195$ (under budget) - For B: $3(19) + 5(30.6) = 57 + 153 = 210$ ✓ - For C: $3(27) + 5(25) = 81 + 125 = 206$ (under budget) - For D: $3(25) + 5(27) = 75 + 135 = 210$ ✓ - For E: $3(65) + 5(6) = 195 + 30 = 225$ (over budget) - For F: $3(55) + 5(4) = 165 + 20 = 185$ (under budget) Only B and D lie exactly on the budget line. **Final answer:** The equation relating pounds of tilapia ($x$) and salmon ($y$) is: $$3x + 5y = 210$$ The graph is a line with intercepts at $x=70$ (when $y=0$) and $y=42$ (when $x=0$). Points B and D lie exactly on this line.