Educational worksheet teaching how to write equations of parallel and perpendicular lines using slope-intercept form.

Let's solve the problem step by step using the information provided in the image.

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Step 1: Fill in the blanks in the "Steps" section

We are given a guide for writing equations of parallel and perpendicular lines. Let's complete the steps:

1. Determine the slope of the parallel or perpendicular line
2. Plug in your $ x $ and $ y $ value in the given ordered pair
3. Substitute the $ x $, $ y $, and $ m $ into the slope-intercept form equation
4. Solve for $ b $
5. Substitute the slope, $ m $, and $ y $-int, $ b $, into the slope-intercept form equation

✔ Completed Steps:
- Step 2: *Plug in*
- Step 3: *x*, *y*, and *m* (or just "x and y values and the slope")
- Step 5: *Substitute*

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Now let’s work through the examples.

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## ✔ Example 1: Write the equation of a line that is parallel to $ y = 4x + 9 $ and passes through $ (0, 2) $

Step 1: Find the slope

- The given line: $ y = 4x + 9 $
- Slope $ m = 4 $
- Since parallel lines have the same slope, the new line also has $ m = 4 $

So:
- $ x = 0 $
- $ y = 2 $
- $ m = 4 $

Step 2: Use slope-intercept form $ y = mx + b $

$$
y = mx + b
$$
$$
2 = 4(0) + b
$$
$$
2 = 0 + b
$$
$$
b = 2
$$

So:
- $ m = 4 $
- $ b = 2 $

Final equation:
$$
y = 4x + 2
$$

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## ✔ Example 2: Write the equation of a line that is perpendicular to $ y = -6x + 12 $ and passes through $ (12, -5) $

Step 1: Find the slope

- Given line: $ y = -6x + 12 $ → slope $ m = -6 $
- Perpendicular lines have opposite reciprocal slopes
- Opposite reciprocal of $ -6 $ is $ \frac{1}{6} $

So:
- $ x = 12 $
- $ y = -5 $
- $ m = \frac{1}{6} $

Step 2: Use slope-intercept form

$$
y = mx + b
$$
$$
-5 = \frac{1}{6}(12) + b
$$
$$
-5 = 2 + b
$$
$$
b = -7
$$

So:
- $ m = \frac{1}{6} $
- $ b = -7 $

Final equation:
$$
y = \frac{1}{6}x - 7
$$

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✔ Final Answers Filled In:

#### Example 1 (Parallel):
- $ x = 0 $, $ y = 2 $, $ m = 4 $
- $ y = mx + b $
- $ 2 = 4(0) + b $
- $ 2 = 0 + b $
- $ 2 = b $
- $ m = 4 $, $ b = 2 $
- $ y = 4x + 2 $

#### Example 2 (Perpendicular):
- $ x = 12 $, $ y = -5 $, $ m = \frac{1}{6} $
- $ y = mx + b $
- $ -5 = \frac{1}{6}(12) + b $
- $ -5 = 2 + b $
- $ -7 = b $
- $ m = \frac{1}{6} $, $ b = -7 $
- $ y = \frac{1}{6}x - 7 $

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✔ Summary:

| Example | Type | Equation |
|--------|------------|----------------------|
| 1 | Parallel | $ y = 4x + 2 $ |
| 2 | Perpendicular | $ y = \frac{1}{6}x - 7 $ |

This completes the worksheet!