Unit 34: Functions and Representations

Day 20 of 30

Slope-intercept form: y = mx + b

6-8Mathematics

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Learning Objective

Students will explore slope-intercept form and y = mx + b through guided practice and application.

Today's Lesson

In this lesson, we'll explore slope-intercept form: y = mx + b. Mathematical thinking develops logical reasoning and problem-solving abilities.

Slope measures the steepness and direction of a line. It's the rate of change: how much y changes when x changes. Formula: slope = (y₂ - y₁)/(x₂ - x₁) = rise/run. Positive slope: line goes up right. Negative slope: goes down right. Zero slope: horizontal line. Undefined slope: vertical line. In real life, slope represents rates: speed (distance/time), cost per item, growth rate. Slope is fundamental to understanding linear relationships and is written as m in y = mx + b!

As you work through today's material, pay attention to the examples and try to identify the patterns or strategies being used. This will help you apply these concepts to new problems.

Take notes on key points and make connections to what you've already learned in previous lessons.

Key Terms
Problem

A mathematical question requiring analysis and solution

Solution

The result obtained by solving a problem

Activities
Instructions
1. Review the example problems for slope-intercept form: y = mx + b. 2. Identify the steps and strategies used. 3. Work through practice problems independently. 4. Compare solutions with a partner.
Materials Needed
  • Notebook
  • Calculator (if needed)
  • Graph paper
Practice Problems
1

Find the slope between (2,3) and (6,11)

Hint: slope = (y₂ - y₁)/(x₂ - x₁)
2

What is the slope of a horizontal line?

Hint: No rise, so rise/run = 0/run.
3

What is the slope of a vertical line?

Hint: No run, so rise/0 is undefined.

Teaching Tip

For advanced learners: Encourage deeper analysis and real-world connections. Consider extension activities that allow students to apply slope-intercept form: y = mx + b to novel situations.

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