Page 2: Understanding Y-Intercepts

This page focuses on the practical identification of y-intercepts from graphs.

Example: Multiple graphs are shown demonstrating y-intercepts in different contexts:

• A water level graph with y-intercept (0, 4.5)
• An elevation graph with y-intercept $0, -10$
• A distance-time graph showing initial positions

Highlight: The y-intercept represents the value of the dependent variable when the independent variable equals zero.

The page emphasizes how y-intercepts can be interpreted in real-world contexts, such as initial water levels or starting elevations.

Page 3: Using Slope Formula to Find Y-Intercepts

This page demonstrates using slope formula to find y-intercept through worked examples.

Example: A detailed worked example shows how to:

1. Calculate slope using two points
2. Use the slope formula with a known point
3. Solve for the y-intercept value

Definition: The slope formula is written as m = $y₂ - y₁$/$x₂ - x₁$, where (x₁,y₁) and (x₂,y₂) are points on the line.

The page includes verification steps to ensure students understand that different points will yield the same y-intercept.

Page 4: Practical Applications

This page applies the concepts to real-world scenarios and data tables.

Example: Problems include:

• Calculating costs for amusement park games
• Tracking savings over time
• Working with larger numerical values

Highlight: The importance of interpreting y-intercepts in context is emphasized through practical scenarios.

The page demonstrates how to handle different types of numerical relationships while maintaining accuracy in calculations.

Page 5: Slope-Intercept Form Applications

This page begins to connect slope and y-intercept concepts to writing complete linear equations.

Definition: The slope-intercept form y = mx + b combines both the slope $m$ and y-intercept $b$ to create a complete linear equation.

Highlight: The page emphasizes how understanding both slope and y-intercept allows for complete representation of linear relationships.

The content builds toward writing equations using real-world data and practical applications.

Writing Equations in Slope-Intercept Form

This section focuses on writing linear equations using slope and y-intercept.

Definition: Slope-intercept form $y = mx + b$ uses the slope $m$ and y-intercept $b$ to define a linear equation.

Highlight: Both y = mx + b and y = b + mx are acceptable forms of slope-intercept form.

Example: Converting linear relationships from tables and points to slope-intercept form.

Practice with Slope-Intercept Form

This page provides additional practice with writing equations in slope-intercept form.

Example: Converting between different forms of linear equations and finding slopes and y-intercepts.

Highlight: Multiple methods can be used to find the components needed for slope-intercept form.

Page 1: Introduction to Slope-Intercept Form

This introductory page sets up the fundamental concepts of slope-intercept form and y-intercepts in linear equations.

Definition: The y-intercept is the point where a line crosses the y-axis, representing the initial value in a linear relationship.

Vocabulary: Slope-intercept form is written as y = mx + b, where m represents the slope and b represents the y-intercept.

The page outlines key learning objectives including:

• Writing y-intercepts as ordered pairs
• Determining y-intercepts from various representations
• Using slope formulas effectively
• Analyzing linear relationships