1. The problem asks to identify which equation corresponds to the given graph. 2. The graph is a straight line with positive slope, crossing the y-axis at (0, 6) and the x-axis at (-3, 0). 3. The slope-intercept form of a line is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 4. From the graph, the y-intercept $b = 6$. 5. The x-intercept is at $x = -3$, so when $y=0$, $x=-3$. 6. Using the two points $(0,6)$ and $(-3,0)$, calculate the slope: $$m = \frac{6 - 0}{0 - (-3)} = \frac{6}{3} = 2$$ 7. So the equation in slope-intercept form is: $$y = 2x + 6$$ 8. Now, check which of the given equations matches this line. 9. Rewrite each given equation in slope-intercept form: - $-6x + y = 18$ $$y = 6x + 18$$ - $x + 3y = 18$ $$3y = -x + 18$$ $$y = -\frac{1}{3}x + 6$$ - $6x + 3y = 18$ $$3y = -6x + 18$$ $$y = -2x + 6$$ - $-6x + 3y = 18$ $$3y = 6x + 18$$ $$y = 2x + 6$$ 10. The last equation $-6x + 3y = 18$ simplifies to $y = 2x + 6$, which matches the graph. **Final answer:** The equation representing the graph is $$-6x + 3y = 18$$.