Worksheet for practicing graphing linear equations in slope-intercept form.

It looks like you've uploaded a worksheet titled "Graphing a Line" that asks students to:

1. Rewrite each equation in slope-intercept form (i.e., $ y = mx + b $).
2. Then, graph the line on the provided coordinate plane.

Since I can't view images directly, I’ll help you solve this type of problem step-by-step based on the typical format of such worksheets. Let’s go through how to approach each problem.

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🔧 Step 1: Understand Slope-Intercept Form

The slope-intercept form of a linear equation is:
$$
y = mx + b
$$
Where:
- $ m $ = slope
- $ b $ = y-intercept

To graph a line:
1. Plot the y-intercept ($ b $) on the y-axis.
2. Use the slope ($ m $) to find another point (rise over run).
3. Draw a straight line through the points.

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📌 Example Problem (Typical Format)

Let’s assume one of the equations is:
> Problem 1: $ 3y - 15 = -6x $

#### Step 1: Solve for $ y $
$$
3y = -6x + 15
$$
Divide both sides by 3:
$$
y = -2x + 5
$$

Now it's in slope-intercept form:
- Slope $ m = -2 $
- Y-intercept $ b = 5 $

#### Step 2: Graph the Line
1. Start at $ (0, 5) $ — this is the y-intercept.
2. Use slope $ -2 $ → go down 2 units, right 1 unit to get to $ (1, 3) $.
3. Draw a line through these two points.

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✔ Let's Solve All Problems (Assuming Standard Equations)

Here are likely equations from your worksheet (based on common problems):

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#### 1. $ 3y - 15 = -6x $
$$
3y = -6x + 15 \Rightarrow y = -2x + 5
$$
- Slope: $ -2 $
- Y-intercept: $ 5 $

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#### 2. $ -3x + 6y = 12 $
$$
6y = 3x + 12 \Rightarrow y = \frac{1}{2}x + 2
$$
- Slope: $ \frac{1}{2} $
- Y-intercept: $ 2 $

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#### 3. $ 5x - 2 = 2y $
$$
2y = 5x - 2 \Rightarrow y = \frac{5}{2}x - 1
$$
- Slope: $ \frac{5}{2} $
- Y-intercept: $ -1 $

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#### 4. $ -4x - 6y = 3 $
$$
-6y = 4x + 3 \Rightarrow y = -\frac{2}{3}x - \frac{1}{2}
$$
- Slope: $ -\frac{2}{3} $
- Y-intercept: $ -\frac{1}{2} $

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#### 5. $ -3y + 9x = 30 $
$$
-3y = -9x + 30 \Rightarrow y = 3x - 10
$$
- Slope: $ 3 $
- Y-intercept: $ -10 $

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#### 6. $ -4y - 8x = 4 $
$$
-4y = 8x + 4 \Rightarrow y = -2x - 1
$$
- Slope: $ -2 $
- Y-intercept: $ -1 $

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#### 7. $ -3x + 6 = 3y $
$$
3y = -3x + 6 \Rightarrow y = -x + 2
$$
- Slope: $ -1 $
- Y-intercept: $ 2 $

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#### 8. $ 3x - 2y = 14 $
$$
-2y = -3x + 14 \Rightarrow y = \frac{3}{2}x - 7
$$
- Slope: $ \frac{3}{2} $
- Y-intercept: $ -7 $

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#### 9. $ -6y + 6 = x $
$$
-6y = x - 6 \Rightarrow y = -\frac{1}{6}x + 1
$$
- Slope: $ -\frac{1}{6} $
- Y-intercept: $ 1 $

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✔ How to Graph Each Line

For each equation:
1. Plot the y-intercept on the graph.
2. Use the slope to find a second point.
- Example: If slope = $ \frac{3}{2} $, go up 3, right 2.
- If slope = $ -\frac{1}{6} $, go down 1, right 6.
3. Draw a straight line through the points.

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💡 Tips:

- Always rewrite in $ y = mx + b $ before graphing.
- Double-check algebra (especially signs and division).
- Use a ruler to draw clean lines.
- Label the graph if required.

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If you can describe or list the exact equations from the worksheet, I can give you the exact answers and graphs for each.

Alternatively, if you want me to generate a completed version of the worksheet, let me know — I can provide the rewritten equations and instructions for plotting each graph.

Would you like that?