Question

Unit 5
Graphing Linear Equations
Lesson 8
Slope-Intercept Form
answers

Answer 1

Certainly! Here’s an overview of the slope-intercept form of a linear equation and how to graph it, along with answers to some common questions:

### Slope-Intercept Form
The slope-intercept form of a linear equation is given by:

\[ y = mx + b \]

Where:
- \( m \) is the slope of the line.
- \( b \) is the y-intercept (the point where the line crosses the y-axis).

### Steps to Graph a Linear Equation in Slope-Intercept Form
1. **Identify the slope and y-intercept** from the equation.
2. **Plot the y-intercept** on the graph (the point \( (0, b) \)).
3. **Use the slope** (rise/run) to find another point.
4. **Draw the line** through the two points.

### Example
Suppose you have the equation:

\[ y = 2x + 3 \]

- **Slope (m)**: 2 (which means rise of 2 and run of 1)
- **Y-intercept (b)**: 3 (the point (0, 3))

### Steps:
1. **Plot the y-intercept**: Start at (0, 3) on the graph.
2. **Use the slope**: From (0, 3), rise 2 units up and run 1 unit to the right to get to (1, 5). Plot this point.
3. **Draw the line**: Connect the two points with a straight line.

### Common Questions and Answers
1. **What does a positive slope indicate?**
- A positive slope means the line rises as you move from left to right.

2. **What does a negative slope indicate?**
- A negative slope means the line falls as you move from left to right.

3. **How do you determine if lines are parallel or perpendicular?**
- **Parallel lines** have the same slope (m).
- **Perpendicular lines** have slopes that are negative reciprocals of each other (e.g., if one slope is \( m \), the other is \( -\frac{1}{m} \)).

4. **How can you convert standard form to slope-intercept form?**
- Start with the standard form: \( Ax + By = C \)
- Solve for \( y \) to get it in the form \( y = mx + b \).

Feel free to ask if you have specific problems or examples you'd like to work through!