Graphing Linear Equations Using Slope-Intercept Form

Algebra 2 Grades High School 13:05 Video
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Lesson Description

Learn how to graph linear equations efficiently using the slope-intercept method. This lesson covers identifying the slope and y-intercept, and using them to plot lines on a coordinate plane.

Video Resource

Graph Linear Functions | Gradient Intercept

Kevinmathscience

Duration: 13:05
Watch on YouTube

Key Concepts

  • Slope-intercept form (y = mx + b)
  • Slope (m) as rise over run
  • Y-intercept (b) as the point where the line crosses the y-axis
  • Positive and negative slopes and their graphical representation

Learning Objectives

  • Identify the slope and y-intercept from a linear equation in slope-intercept form.
  • Graph a linear equation using the slope-intercept method.
  • Interpret the meaning of positive and negative slopes.
  • Manipulate equations to isolate 'y' and express them in slope-intercept form.

Educator Instructions

  • Introduction (5 mins)
    Briefly review the concept of linear equations and their standard form. Introduce the slope-intercept form (y = mx + b) and explain the significance of 'm' (slope) and 'b' (y-intercept).
  • Video Presentation (10 mins)
    Play the YouTube video "Graph Linear Functions | Gradient Intercept" by Kevinmathscience. Instruct students to take notes on the key steps and examples provided.
  • Guided Practice (15 mins)
    Work through example problems on the board, demonstrating how to identify the slope and y-intercept from an equation and use them to graph the line. Emphasize the 'rise over run' concept for slope. Cover examples with positive, negative, and fractional slopes.
  • Independent Practice (15 mins)
    Assign practice problems where students graph linear equations using the slope-intercept method. Circulate the classroom to provide assistance and answer questions.
  • Wrap-up and Discussion (5 mins)
    Review the key concepts and address any remaining questions. Preview the next lesson on finding the equation of a line given two points.

Interactive Exercises

  • Slope-Intercept Matching
    Provide students with a set of linear equations and a set of graphs. Students must match each equation to its corresponding graph.
  • Graphing Race
    Divide students into teams and give each team a linear equation. The first team to correctly graph the equation on a whiteboard wins.

Discussion Questions

  • How does changing the slope affect the steepness and direction of the line?
  • What is the significance of the y-intercept in a real-world context (e.g., cost of a service with a flat fee and hourly rate)?
  • Can you graph a vertical line using the slope-intercept method? Why or why not?

Skills Developed

  • Identifying slope and y-intercept
  • Graphing linear equations
  • Interpreting slope
  • Problem-solving

Multiple Choice Questions

Question 1:

What is the slope of the line y = 3x - 2?

Correct Answer: 3

Question 2:

What is the y-intercept of the line y = -2x + 5?

Correct Answer: 5

Question 3:

A line has a slope of 2 and a y-intercept of -1. Which equation represents this line?

Correct Answer: y = 2x - 1

Question 4:

Which direction does a line with a negative slope go as you move from left to right?

Correct Answer: Downward

Question 5:

What is the 'rise' in the slope-intercept form?

Correct Answer: The change in y

Question 6:

If a line has a slope of 0, what kind of line is it?

Correct Answer: Horizontal

Question 7:

The equation is 2y = 4x + 6, what is the slope?

Correct Answer: 2

Question 8:

Which point does the line y = x - 4 cross the y-axis?

Correct Answer: (0, -4)

Question 9:

A line's slope is 5/2. For every 2 units you move to the right, how many units do you move up?

Correct Answer: 5

Question 10:

What is the correct process to determine the slope?

Correct Answer: Rise/Run

Fill in the Blank Questions

Question 1:

The slope-intercept form of a linear equation is y = ____ + b.

Correct Answer: mx

Question 2:

The 'm' in y = mx + b represents the ____ of the line.

Correct Answer: slope

Question 3:

The 'b' in y = mx + b represents the ____-intercept.

Correct Answer: y

Question 4:

A line with a positive slope goes ____ as you move from left to right.

Correct Answer: up

Question 5:

A line with a negative slope goes ____ as you move from left to right.

Correct Answer: down

Question 6:

The slope is calculated as the ____ over the run.

Correct Answer: rise

Question 7:

If the slope is -4, then you go 4 units ____.

Correct Answer: down

Question 8:

If an equation is 3y = 6x + 9, the y-intercept is ____.

Correct Answer: 3

Question 9:

If an equation is 3y = 6x + 9, the slope is ____.

Correct Answer: 2

Question 10:

A horizontal line has a slope of ____.

Correct Answer: 0

Educational Standards

A2.A.1.7:Represent and evaluate mathematical models using systems of linear equations with a maximum of three variables. Graphing calculators or other appropriate technology may be used. A2.F.1:Understand functions as descriptions of covariation (how related quantities vary together).

Teaching Materials

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