Graphing & Writing Linear Equations - Connect the Points, Write the Rules!
Welcome to our learning module on graphing and writing linear equations! In this module, you’ll start by exploring proportional linear relationships, which are a key concept in understanding how variables can change together at a constant rate. Through video lessons, you’ll learn to graph these relationships, identify when they are proportional, and interpret the slope of the line as the unit rate. This foundation will help you see how linear relationships connect values in a clear and predictable way, both in math and in real-world scenarios.
As you advance, you’ll dive into comparing proportional relationships across different formats, such as graphs, tables, and equations. You’ll practice finding the slope of a line and explore how it represents the rate of change in a linear relationship. By using similar triangles, you’ll see why the slope between any two points on a line remains constant, which is essential for understanding the behavior of linear equations and making comparisons between different proportional relationships.
In the final part of the module, you’ll learn how to graph linear equations using slope-intercept form. This skill allows you to quickly and accurately draw a line on a graph based on its slope and y-intercept. By the end of this module, you’ll be equipped to write, interpret, and graph linear equations, giving you a powerful tool to analyze and model relationships between variables.
Lesson Objective: Students will be able to graph a linear equation using a table and will understand that lines represent solutions of linear equations.
Essential Question: What will ALL graphs of linear equations have in common?
Lesson Objective: Students will understand the connection between proportional and linear relationships by identifying key features of both types of relationships. They will learn to find and interpret the slope of proportional relationships, graph these relationships on the coordinate plane, and compare multiple proportional relationships to determine similarities and differences in their slopes and rates of change.
Essential Question: What is the relationship between slope and unit rate?
Check for Understanding: Test your understanding with these end-of-lesson practice problems to reinforce your skills and master the concept!
Lesson Objective: Students will be able to find the slope of a line using a graph, points, and a table of values.
Essential Question: What does the slope of a line tell you about the line?
Check for Understanding: Test your understanding with these end-of-lesson practice problems to reinforce your skills and master the concept!
Lesson Objective: Students will be able to identify the slope and y-intercept of linear equations from their graphs. They will learn how to use the slope and y-intercept to graph linear equations accurately on the coordinate plane, reinforcing their understanding of the relationship between these elements and the equation of a line.
Essential Question: What is true about the y-intercept of ANY linear equation?
Check for Understanding: Test your understanding with these end-of-lesson practice problems to reinforce your skills and master the concept!