LF - Linear Functions Module Overview

Linear Functions Module Overview

Introduction

Have you ever baked cookies for a huge group of people or wondered how the lunchroom ladies knew how much of each ingredient to use in their humongous batch of cookies for thousands of students? Proportions come into play when looking at applications like this. In this module, we are going to take a look at proportional relationships and recognize the unit rate as our slope, or rate of change. We are even going to discover why we can use the infamous y=mx+b to write an equation of our linear function. Remember those similar triangles we studied? We'll use these similar triangles to help us derive this equation, y=mx+b. We'll also learn how to determine if a function is linear. We'll be able to look at a function's graph or at a function's equation to make this linear vs. nonlinear decision. In future courses, you'll learn more about the nonlinear functions, so it is vital to begin to recognize which ones are linear and which ones are not.

Essential Questions

• How do we graph proportional relationships?
• How can we find the slope of a line from a graph?
• How do we know the slope of a line when given an equation?
• How do we know whether a function is linear or non-linear?

Key Terms

The following key terms will help you understand the content in this module.

Intersecting Lines - Two lines that cross each other. Lines intersect at one point unless the lines fall directly on top of each other (in which case they are essentially the same line and are sometimes called coincidental).

Origin - The point of intersection of the vertical and horizontal axes of a Cartesian plane. The coordinates of the origin are (0, 0).

Proportional Relationships - A relationship between two equal ratios.

Slope - The "steepness" of a line. The slope of a line can be found directly when a linear equation is in slope-intercept form (y = mx + b). In this form, the slope is the coefficient of x and is represented by the letter m. The slope of a line can also be found by determining the ratio of the "rise" to the "run" between two points on the graph. In other words, slope measures how much the line rises vertically given a particular run or horizontal distance.

Unit Rate - A comparison of two measurements in which the second term has a value of 1. Unit rates are used to compare the costs of items in a grocery store.

 IMAGE SOURCE: CLIPART.COM