how to graph the linear function 10x+5y=-20

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.

Learn how to graph the linear equation 10x + 5y = -20 using step-by-step instructions. This problem explains the conversion to slope-intercept form, finding intercepts, and drawing the line. Perfect for Grades 7-10 students learning algebra and graphing.

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