To graph the linear equation $10x + 5y = -20$, follow these steps:

1. Convert to slope-intercept form (if desired)

We can rearrange the equation into the slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

$10x + 5y = -20$

First, solve for $y$: $5y = -10x - 20$ $y = -2x - 4$

Now, we know that the slope $m = -2$ and the y-intercept $b = -4$. So the equation becomes: $y = -2x - 4$

2. Find the y-intercept

The y-intercept is where the graph crosses the y-axis. To find this, set $x = 0$: $y = -2(0) - 4 = -4$ So, the point is $(0, -4)$.

3. Find the x-intercept

The x-intercept is where the graph crosses the x-axis. To find this, set $y = 0$: $0 = -2x - 4$ $2x = -4$ $x = 2$ So, the x-intercept is $(2, 0)$.

4. Plot the intercepts

Plot the points $(0, -4)$ and $(2, 0)$ on the coordinate plane.

5. Draw the line

Once you've plotted the intercepts, draw a straight line through them to graph the equation.

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Would you like more details on the graphing process, or how to calculate the slope and intercept?

Here are some related questions for further exploration:

1. How can you graph other forms of linear equations?
2. What is the significance of the slope in a linear function?
3. How do you find the slope between two points on a line?
4. How does the y-intercept affect the graph of a line?
5. What is the general form of a linear equation, and how do you convert it?

Tip: Always check your intercepts by plugging them back into the original equation to verify accuracy.