MLRF - Modeling Linear Relationships & Functions Overview

Modeling Linear Relationships & Functions Overview

In this module, you will learn to analyze the connections between proportional and non-proportional lines and equations and be able to relate their graphs to their solution sets in the coordinate plane.  You will also interpret, write, graph, and solve linear functions in different forms, depending upon the given context.  You will also learn to describe the properties of functions to define, evaluate, and compare relationships, and use functions and their graphs to model and explain real-life phenomena.

Essential Questions

  1. How do we graph proportional relationships?
  2. How can we find the slope of a line from a graph?
  3. How do we know the slope of a line when given an equation?
  4. How do we know whether a function is linear or non-linear?
  5. What is a function and how do I use it to model real-world situations?
  6. How do I interpret the parts of a function in the context of the problem?

Key Terms

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

Origin: The point where the x-axis and y-axis intersect on the coordinate plane

Relation:  A relation is a relationship between the x-values and y-values of ordered pairs. 

Function: An input-output relationships that has exactly one output for each input.       

Vertical Line Test:  If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.

Input: The independent variable, x in the ordered pair, the input, and the domain.

Output: The dependent variable, y in the ordered pair, the output, and the range.

Domain: The set of all x values in a function.

Range: The set of all y values in a function.

Linear Function: A function whose equation creates a straight line on a graph. 

Slope: The steepness of a line.  This can be positive, negative, or horizontal(0 slope).

Unit Rate: A rate in which the x value (or the 2nd value) is one.

Rate of change: This is interchangeable with slope and represents  how fast a graph's y-variable changes compared to its x-variable. We use the rise over run formula to find the rate of change.

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