# Lesson Plan: The Slope Formula

## Lesson Objectives

• Define the slope formula and how to use it
• Develop an algebraic understanding of slope

## Common Core Standards

• CCSS.MATH.CONTENT.8.EE.B.6: Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
• CCSS.MATH.CONTENT.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.

## 1. Warm-up (5 minutes)

Review the previous lesson on types of slopes (https://www.media4math.com/LessonPlans/TypesOfSlope). Ask students to identify the slope of various line segments shown on the board or projector. Make the following observations:

• Previous ways of calculating slope were more geometric and visual (coordinate grids, measuring the rise and run).
• What if the only information you have about two points are their coordinates? How could you calculate the slope?

## 2. Teach (15 minutes)

Show students the definition of the slope formula: https://www.media4math.com/library/22185/asset-preview

Elaborate on the following points:

• The slope formula provides an algebraic way of calculating slope.
• The algebraic symbol for slope is m.
• The slope formula uses the coordinates of the two points to calculate the slope.
• The slope formula is the ratio of the change in the y-coordinates (the rise) to the change in the x-coordinates (the run)

Relate this to the concept of slope as the rise over the run (https://www.media4math.com/LessonPlans/WhatIsSlope).

## Engage

Explain why someone would use the slope formula:

• To precisely calculate the slope between any two points on a line
• To determine if two lines are parallel (same slope) or perpendicular (negative reciprocal slopes)
• To write the equation of a line when given two points it passes through

## Explore

Show students the following math examples using the slope formula:

Additional examples can be found here: https://www.media4math.com/MathExamplesCollection--SlopeFormula to guide students through solving examples using the slope formula. Project or distribute the step-by-step examples, and have students follow along as you solve them together.

You can also show the following video tutorials using the slope formula, which go through a step-by-step process for using the slope formula:

## Explain

Break down the slope formula and discuss how to plug in coordinates to find the slope. Emphasize the importance of the order of the points and how it affects the sign of the slope.

## 3. Review (5 minutes)

Review slope and the slope formula with this presentation: https://www.media4math.com/library/21537/asset-preview.

## 4. Assess (10 minutes)

Distribute a 10-question quiz where students find the slope between various pairs of points. Include questions that cover positive, negative, zero, and undefined slopes. This assessment will help you evaluate their understanding of the slope formula and their ability to apply it correctly.

### Slope Quiz (10 questions)

1. Find the slope of the line passing through the points (2, 3) and (5, 7).
2. Calculate the slope of the line passing through the points (-4, 2) and (3, -5).
3. Determine the slope of the line passing through the points (0, 0) and (6, 0).
4. Find the slope of the line passing through the points (1, 4) and (1, -2).
5. Calculate the slope of the line passing through the points (-2, 5) and (4, 5).
6. Determine the slope of the line passing through the points (3, -1) and (3, 4).
7. Find the slope of the line passing through the points (0, 0) and (0, 0).
8. Calculate the slope of the line passing through the points (2, -3) and (-1, 4).
9. Determine the slope of the line passing through the points (5, 2) and (-3, -4).
10. Find the slope of the line passing through the points (4, 0) and (0, 3).

Throughout the lesson, encourage students to ask questions and provide clear explanations. Reinforce the connection between the slope formula and the visual representation of slope on a graph.