Linear Functions and Family Groups

These web-based activities were developed, during summer sessions from 1997 through 1999, by students at Mainland High School, located in Daytona Beach, FL. As part of Mainland's CCTT grant, the students were given permission by the book's publisher to convert the ancillary materials of the County's adopted Algebra 1 Textbook into html format.

Linear Functions and Family Groups

A parent graph is the basic representation of a function. In Chapter 2, you are learning about linear functions f(x) = x which is a straight line passing through the origin with a slope of 1. All lines are a variation of this parent function created by multiplying x by a constant (changing the slope) or adding/subtracting a constant (changing the y-axis intercept). It goes without saying, that all lines are straight.

A group of lines having the same slope (but diferent y-axis intercepts) form a subfamily of parallel lines.

Horizontal lines (slope equaling zero) form another subfamily. These lines are called constant functions since f(x), aka y, always has the same constant value, regardless of the value of x.

Practice your understanding by sketching on co-ordinate planes a family of parallel lines and a family of horizontal lines. State each line's equation.