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Use functions to model relationships between quantities.
4.
Construct a function to model a linear relationship between two quantities. Determine the rate of change  and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

• Distance-Time Graphs
This tutorial is designed to help students understand the concept of slope and how distance-time graphs represent the relationship of collected data.
• Functions - Standards 4 and 5 Curriculum Guide
The Utah State Office of Education (USOE) and educators around the state of Utah developed these guides for Mathematics Grade 8 Cluster "Use Functions to Model Relationships Between Quantities." / Standards 4 and 5
• Graphit
With this interactive applet students are able to create graphs of functions and sets of ordered pairs on the same coordinate plane.
• Graphs and Functions
This lesson plan is designed to help the student understand how to plot functions on the Cartesian plane and how the graphing of functions leads to lines and parabolas.
• Introduction to Functions
This lesson introduces students to functions and how they are represented as rules and data tables. They also learn about dependent and independent variables.
• Linear Function Machine
By putting different values into the linear function machine students will explore simple linear functions.
• Linear Functions and Slope
This lesson asks students to examine line and slope in understanding linear functions.
• Linear Models
This lesson helps the student understand linear models by using real-world examples of change over time in both graphic and equation form.
• More Complicated Functions: Introduction to Linear Functions
This lesson is designed to reinforce the concept of linear functions and ask students to write functions using English, tables and algebra.
• Proportional Reasoning
In this lesson students explore proportions by examining proportional relationships, absolute and relative comparisons, and looking at graphs to learn about these relationships.
• Slope Slider
This website's applet lets the student manipulate a linear function in order to better understand the relationship between slope and intercept in the Cartesian coordinate system.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Office of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Office of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.