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Let's go over the given linear equations and describe how to graph each line.

### 16. \( y = x + 2 \)
This is in slope-intercept form \( y = mx + b \), where:
- **Slope (m)** = 1
- **Y-intercept (b)** = 2

To graph:
1. Start at (0, 2) on the y-axis.
2. Use the slope: rise 1 unit and run 1 unit to the right to find the next point.
3. Draw the line through these points.

### 18. \( y = \frac{1}{2}x - 1 \)
This is also in slope-intercept form:
- **Slope (m)** = \( \frac{1}{2} \)
- **Y-intercept (b)** = -1

To graph:
1. Start at (0, -1) on the y-axis.
2. From there, rise 1 unit and run 2 units to the right to plot the next point.
3. Draw the line through the points.

### 20. \( y - 3 = \frac{1}{3}(x - 3) \)
This equation is in point-slope form \( y - y_1 = m(x - x_1) \), where:
- **Slope (m)** = \( \frac{1}{3} \)
- Point \( (x_1, y_1) \) = (3, 3)

To graph:
1. Start at point (3, 3).
2. Use the slope: rise 1 unit and run 3 units to the right to find the next point.
3. Draw the line through these points.

### 22. \( y + 4 = x - 5 \)
First, rewrite the equation in slope-intercept form:
\[
y = x - 5 - 4 \implies y = x - 9
\]
This is a slope-intercept form equation:
- **Slope (m)** = 1
- **Y-intercept (b)** = -9

To graph:
1. Start at (0, -9) on the y-axis.
2. From there, rise 1 unit and run 1 unit to the right to find the next point.
3. Draw the line through the points.

Would you like further explanation on any of these steps or the graphing process? Here are some related questions to expand on this:

1. How can you convert point-slope form to slope-intercept form?
2. What does the slope of a line represent graphically?
3. How do you find the slope of a line from two given points?
4. What is the significance of the y-intercept in real-world scenarios?
5. How would you graph lines with negative slopes?

**Tip**: Always plot at least two points to ensure accuracy when drawing the line for a given equation.

Graph the following linear equations: y = x + 2, y = (1/2)x - 1, y - 3 = (1/3)(x - 3), and y + 4 = x - 5.

This tutorial covers how to graph linear equations, including y = x + 2, y = (1/2)x - 1, and more. Learn about slope, intercepts, and graphing techniques. Suitable for students in Grades 8-10.

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