Graphing lines using slope and point on coordinate planes.

To solve the problem of drawing lines through given points with specified slopes, we need to understand how slopes work and how to apply them on a graph. Let's break it down step by step.

Key Concepts:

1. Slope Definition: The slope \( m \) of a line is defined as the ratio of the vertical change (rise) to the horizontal change (run). Mathematically, \( m = \frac{\text{rise}}{\text{run}} \).
2. Positive Slope: A positive slope means the line rises as you move from left to right.
3. Negative Slope: A negative slope means the line falls as you move from left to right.
4. Zero Slope: A zero slope means the line is horizontal.
5. Undefined Slope: An undefined slope means the line is vertical.

Steps to Solve:

For each part of the worksheet, we are given a point and a slope. We need to draw a line through the given point with the specified slope. Here’s how to do it:

#### General Procedure:
1. Identify the given point.
2. Use the slope to determine the rise and run.
- If the slope is \( m = \frac{a}{b} \), then rise = \( a \) and run = \( b \).
3. Starting from the given point, move up (or down) by the rise and right (or left) by the run to find another point on the line.
4. Draw a straight line through the original point and the new point.

Example Walkthrough:

Let’s solve one of the problems as an example. Suppose we have:

- Point: (2, 3)
- Slope: \( m = \frac{1}{2} \)

#### Steps:
1. Identify the Point: The point is (2, 3).
2. Interpret the Slope: The slope \( m = \frac{1}{2} \) means rise = 1 and run = 2.
3. Find Another Point:
- Starting at (2, 3), move up 1 unit and right 2 units.
- New point: (2 + 2, 3 + 1) = (4, 4).
4. Draw the Line: Draw a straight line through the points (2, 3) and (4, 4).

Applying to All Problems:

Repeat the above steps for each problem in the worksheet. Here’s a summary for each slope type:

1. Positive Slope: Move up (rise) and right (run).
2. Negative Slope: Move down (rise) and right (run), or up and left.
3. Zero Slope: Draw a horizontal line.
4. Undefined Slope: Draw a vertical line.

Final Answer:

Since the worksheet involves multiple problems, the solution involves drawing lines for each given point and slope. The exact coordinates of the points and slopes are not provided in the question, but the method described above can be applied to any problem on the worksheet.

If you need help with a specific problem or need further clarification, feel free to ask!

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\boxed{\text{Follow the steps above to draw the lines for each problem.}}
$$