Worksheet for practicing graphing linear equations on coordinate grids.

It looks like you've uploaded a worksheet titled "Graphing Linear Equations", which contains several linear equations to graph on coordinate planes. However, since I cannot view or access images directly, I can't see the specific equations or graphs.

But based on the layout and typical structure of such worksheets, here’s how you can solve this type of problem:

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🔍 How to Graph Linear Equations Step-by-Step

Each equation should be graphed on its own coordinate plane (grid). Here's the general method:

#### 1. Identify the Equation Form
Linear equations are usually in one of these forms:
- Slope-intercept form: $ y = mx + b $
- Standard form: $ Ax + By + C = 0 $
- Point-slope form: $ y - y_1 = m(x - x_1) $

If it's not in slope-intercept form, convert it.

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#### 2. Convert to Slope-Intercept Form (if needed)

For example:
- $ 3x + y = 0 $ → $ y = -3x $
- $ 2x - 4y = 8 $ → Solve for $ y $:
$$
-4y = -2x + 8 \Rightarrow y = \frac{1}{2}x - 2
$$

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#### 3. Plot the Y-Intercept ($b$)
- This is where the line crosses the y-axis.
- Example: If $ y = 2x + 1 $, start at $ (0, 1) $.

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#### 4. Use the Slope ($m$) to Find Another Point
- Slope = rise over run.
- Example: For $ m = \frac{3}{2} $, go up 3, right 2 from the y-intercept.

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#### 5. Draw a Straight Line Through the Points

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✔ Examples Based on Common Problems

Let’s assume some of the equations on your sheet might be:

1. $ y = \frac{1}{2}x + 1 $
- Y-intercept: $ (0, 1) $
- Slope: $ \frac{1}{2} $ → up 1, right 2
- Plot points: $ (0,1), (2,2), (-2,0) $ → draw line

2. $ y = 2x - 3 $
- Y-intercept: $ (0, -3) $
- Slope: 2 → up 2, right 1

3. $ 3x + y = 0 $ → $ y = -3x $
- Passes through origin $ (0,0) $
- Slope: -3 → down 3, right 1

4. $ x + y = 2 $ → $ y = -x + 2 $
- Y-intercept: $ (0,2) $
- Slope: -1 → down 1, right 1

5. $ x = 2 $ → vertical line at $ x = 2 $
- Draw a vertical line through $ x = 2 $

6. $ y = 0 $ → horizontal line along the x-axis

7. $ 4x - 10y = 20 $ → divide by 2: $ 2x - 5y = 10 $
- Solve for $ y $: $ -5y = -2x + 10 $ → $ y = \frac{2}{5}x - 2 $
- Y-intercept: $ (0, -2) $
- Slope: $ \frac{2}{5} $ → up 2, right 5

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📌 Tips:

- Always label axes.
- Use a ruler for straight lines.
- Check if the line passes through two known points.
- For vertical/horizontal lines, remember:
- $ x = a $ → vertical line
- $ y = b $ → horizontal line

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🧩 Final Advice:

Since I can’t see your image, please describe or list the equations from the worksheet, and I’ll help you graph each one step-by-step!

Or, if you'd like, you can write out the equations, and I’ll provide coordinates to plot and instructions for each.