Question: Which of the following equations does the graph below represent? y 20 16 12 8 4 0 -4 -8 -12 -16 -20 x -20 -16 -12 -8 -4 4 8 12 16 20 Answer -3x - 6y = 36 x + 6y = 36 -3x + 6y = 36 3x + 6y = 36 Submit Answer Graph shape and math: A straight increasing line in the center-left graph crosses the y-axis at about 6 and the x-axis at about -12, extending from bottom-left to top-right; this matches the equation 3x - 6y = -36, equivalent to -3x + 6y = 36, so position_hint = center.

1. **State the problem:** We need to determine which equation corresponds to the given graph. 2. **Analyze the graph:** The line crosses the y-axis at about $6$ and the x-axis at about $-12$. 3. **Recall the intercept form of a line:** $$\frac{x}{a} + \frac{y}{b} = 1$$ where $a$ is the x-intercept and $b$ is the y-intercept. 4. **Substitute the intercepts:** $$\frac{x}{-12} + \frac{y}{6} = 1$$ 5. **Multiply both sides by the common denominator $-12 \times 6 = -72$ to clear fractions:** $$-6x - 12y = -72$$ 6. **Simplify by dividing both sides by $-6$:** $$\cancel{-6}x + \cancel{-12}y = \cancel{-72}$$ becomes $$x + 2y = 12$$ 7. **Check given options:** None match $x + 2y = 12$ exactly, so let's check the original equations by plugging intercepts. 8. **Check $-3x - 6y = 36$ at $x=0$:** $$-3(0) - 6y = 36 \Rightarrow -6y = 36 \Rightarrow y = -6$$ Does not match y-intercept $6$. 9. **Check $x + 6y = 36$ at $x=0$:** $$0 + 6y = 36 \Rightarrow y = 6$$ Matches y-intercept. At $y=0$: $$x + 6(0) = 36 \Rightarrow x = 36$$ Does not match x-intercept $-12$. 10. **Check $-3x + 6y = 36$ at $x=0$:** $$-3(0) + 6y = 36 \Rightarrow 6y = 36 \Rightarrow y = 6$$ Matches y-intercept. At $y=0$: $$-3x + 0 = 36 \Rightarrow x = -12$$ Matches x-intercept. 11. **Check $3x + 6y = 36$ at $x=0$:** $$3(0) + 6y = 36 \Rightarrow y = 6$$ Matches y-intercept. At $y=0$: $$3x + 0 = 36 \Rightarrow x = 12$$ Does not match x-intercept. 12. **Conclusion:** The equation that matches both intercepts is $$-3x + 6y = 36$$ **Final answer:** $-3x + 6y = 36$