Ohio Resource Center
Lessons
More Complicated Functions: Introduction to Linear Functions
Discipline
Mathematics
8
Professional Commentary

This lesson helps students who are not already familiar with the slope-intercept form of a linear function, y = mx + b, to analyze how the values of m and b correspond to changes in y as x systematically increases. This analysis helps students identify linear function rules involving two operations. A function machine applet provides some engaging practice in determining these compound function rules. (sw)

Common Core State Standards for Mathematics
Standards for Mathematical Practice
CCSS.Math.Practice.MP7
Look for and make use of structure.
Functions
Define, evaluate, and compare functions.
8.F.A.1
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
8.F.A.3
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
Use functions to model relationships between quantities.
8.F.B.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.
Ohio Mathematics Academic Content Standards (2001)
Patterns, Functions and Algebra Standard
Benchmarks (5–7)
B.
Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules.
E.
Use rules and variables to describe patterns, functions and other relationships
L.
Analyze functional relationships, and explain how a change in one quantity results in a change in the other.
Benchmarks (8–10)
C.
Translate information from one representation (words, table, graph or equation) to another representation of a relation or function.
J.
Describe and interpret rates of change from graphical and numerical data.
2.
Use words and symbols to describe numerical and geometric patterns, rules and functions.
1.
Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions.
10.
Analyze linear and simple nonlinear relationships to explain how a change in one variable results in the change of another.