To graph the equation $x + 2y = -6$, you can find points to plot by solving for $y$ for different values of $x$.

Let's rearrange the equation to solve for $y$: $2y = -6 - x$ $y = \frac{-6 - x}{2}$

Now, we can pick some values for $x$ and solve for $y$.

1. When $x = 0$: $y = \frac{-6 - 0}{2} = \frac{-6}{2} = -3$ So one point is $(0, -3)$.

2. When $x = -6$: $y = \frac{-6 - (-6)}{2} = \frac{-6 + 6}{2} = 0$ So another point is $(-6, 0)$.

3. When $x = -4$: $y = \frac{-6 - (-4)}{2} = \frac{-6 + 4}{2} = \frac{-2}{2} = -1$ So a third point is $(-4, -1)$.

You can use these points $(0, -3), (-6, 0), (-4, -1)$ to plot the line. You can choose additional points if you want a more accurate graph.

Do you need more details or have any questions?

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Here are 5 related questions:

1. What is the slope of the line represented by $x + 2y = -6$?
2. How do you convert the equation $x + 2y = -6$ into slope-intercept form?
3. What is the x-intercept of the line $x + 2y = -6$?
4. How would the graph of $x + 2y = -6$ change if the equation became $x + 2y = -4$?
5. What are the general steps to graph a linear equation in two variables?

Tip: When graphing linear equations, it's often useful to find both the x- and y-intercepts for easy plotting.