# Lesson Plan: Graphing Linear Equations

## Lesson Objectives:

- Plot points on the coordinate plane
- Identify the slope and y-intercept of a linear equation
- Graph linear equations using the slope-intercept form
- Interpret the meaning of slope and y-intercept in real-life situations

## Common Core Standards:

- 8.EE.B.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph.
- 8.EE.B.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane.

## Prerequisite Skills:

- Plotting points on the coordinate plane
- Understanding of slope and y-intercept concepts

## Key Vocabulary:

- Coordinate plane
- Ordered pair
- Slope
- y-intercept
- Slope-intercept form

## Warm-up Activity (5 minutes)

For students that need to review graphing points on the coordinate plane review the first example from this video:

__https://www.media4math.com/library/39514/asset-preview__

Engage students by asking them to plot the following points on a coordinate plane:

(1, 2)

(2, 4)

(3, 6).

Use this Desmos activity to graph the points and ask students to notice any patterns.

__https://www.desmos.com/calculator/cq834lfyfp__

Then ask them to find additional coordinates that continue the pattern.

## Teach (20 minutes)

### Definitions

Use the following video definitions to define key terms:

- The slope-intercept form of a linear equation:
__https://www.media4math.com/library/74604/asset-preview__ - The y-intercept:
__https://www.media4math.com/library/74608/asset-preview__ - The slope:
__https://www.media4math.com/library/74617/asset-preview__

### Examples

Demonstrate how to identify the slope and y-intercept from a given linear equation.

- Start by showing this video about the slope-intercept form:
__https://www.media4math.com/library/39543/asset-preview__ - Provide examples of graphing linear equations using the slope-intercept form. Use this slide show, which focuses on given the slope and the y-intercept, graph the linear equation
__https://www.media4math.com/library/slideshow/math-examples-slope-intercept-form__ - Have students use this Desmos activity to explore the slope-intercept form:
__https://www.media4math.com/library/40088/asset-preview__ - Here is the corresponding worksheet for this Desmos activity:
__https://www.media4math.com/library/40089/asset-preview__

## Review (10 minutes)

- Try this drag-and-drop game, which focuses on linear equations:
__https://www.media4math.com/library/4829/asset-preview__ - Encourage students to graph linear equations using the slope-intercept form.
- Address any misconceptions or questions that arise during the review.

## Assess (10 minutes)

Administer a 10-question quiz to assess students' understanding of graphing linear equations. The quiz should include questions on plotting points, identifying slope and y-intercept, graphing linear equations, and interpreting slope and y-intercept in real-life situations.

### Quiz

- Plot the points (1, 2), (-2, -1), and (3, 4) on the coordinate plane.
- Identify the slope and y-intercept of the equation y = 2x + 3.
- Graph the equation y = -1/2x + 4 on the coordinate plane.
- If the slope of a linear equation is 3 and the y-intercept is -2, what is the equation?
- Interpret the meaning of the slope and y-intercept in the equation y = 0.5x + 10. You save fifty cents a day in a piggy bank that already has an amount of money in it.
- A line passes through the origin and through (4, 9). What is its equation?
- Determine if the point (3, -1) lies on the line represented by the equation y = 2x - 5.
- Graph the equation 3y = 6x - 9 on the coordinate plane.
- Explain the relationship between the slope of a line and its steepness.
- This equation represents a car slowing down every second at a constant speed (in miles per hour): y = -5x +50. What is the car's initial speed? What does the slope represent?

### Answers

- Slope = 2, y-intercept = 3
- y = 3x - 2
- The slope represents the 50 cents saved a day. The y-intercept is the amount of money initially in the piggy bank (\$10).
*y*= 9/4*x*- No, the point (3, -1) does not lie on the line.
- The steeper the line, the greater the slope value (positive or negative).
- Initial speed is 50 mph. The car slows down by 5 mph every second.

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