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Unit 5

Graphing Linear Equations
Lesson 8
Slope-Intercept Form
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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!