https://file.aiquickdraw.com/mathbot/file/1730478125764tzawm14h.jpg

To graph the line \(5x = -2y - 2\), let's follow these steps:

### Step 1: Rewrite the Equation in Slope-Intercept Form
To make it easier to plot, we’ll rearrange this equation to isolate \(y\).

1. Start with:
   \[
   5x = -2y - 2
   \]

2. Add \(2y\) to both sides:
   \[
   5x + 2y = -2
   \]

3. Subtract \(5x\) from both sides:
   \[
   2y = -5x - 2
   \]

4. Finally, divide by 2 to solve for \(y\):
   \[
   y = -\frac{5}{2}x - 1
   \]

Now, the equation is in the form \(y = mx + b\), where \(m = -\frac{5}{2}\) (the slope) and \(b = -1\) (the y-intercept).

### Step 2: Identify Points to Plot
1. **Y-intercept**: When \(x = 0\), \(y = -1\). So, one point is \((0, -1)\).

2. **Another Point**: Use the slope, which is \(-\frac{5}{2}\). This means that for every increase of 2 in \(x\), \(y\) decreases by 5.

   - Starting from \((0, -1)\):
     - If \(x = 2\), then \(y = -1 - 5 = -6\).
   - So, another point is \((2, -6)\).

### Step 3: Plot the Points and Draw the Line
1. **Points to Plot**: Plot the points \((0, -1)\) and \((2, -6)\) on the graph.
2. **Draw the Line**: Connect these points to draw the line representing the equation \(5x = -2y - 2\).

Would you like further details on the plotting process or have any questions?

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### Additional Questions to Expand Understanding:
1. What are the steps to convert any linear equation into slope-intercept form?
2. How do you interpret the slope of a line geometrically on a graph?
3. Can you find another point on this line if \(x = -2\)?
4. How would the graph change if the equation were \(5x = 2y - 2\) instead?
5. What does the y-intercept tell you about where the line crosses the y-axis?

**Tip:** When graphing a line, always look for two points and then use the slope to ensure accuracy.

Use technology to find points and graph the line 5x = -2y - 2, following the instructions below.

Learn how to graph the linear equation 5x = -2y - 2. Follow step-by-step instructions to convert it into slope-intercept form, identify key points, and plot the line accurately. Ideal for students in Grades 8-10.

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