Linear Functions

This chapter takes the general language of functions from Chapter 1 and applies it to the simplest family of all: the functions whose rate of change never varies. It begins with what makes a function linear and how to write one from a slope and a point, a pair of points, or a description in words, then turns to what those formulas look like on a grid — how slope and intercept move a line, when two lines are parallel or perpendicular, and where they cross. It closes by pointing the tools outward: building linear models for real situations and deciding how well a line fits data that only approximately follows one.

Sections

• Linear Functions — recognizing a function with a constant rate of change, computing slope from two points, writing a linear function in slope-intercept and point-slope form, interpreting slope and initial value in context, and distinguishing increasing, decreasing, and constant behavior.
• Graphs of Linear Functions — graphing a line from its intercepts, from slope-intercept form, and by transforming the identity function, writing the equation of a line from its graph, horizontal and vertical lines, parallel and perpendicular lines, and finding the point where two lines intersect.
• Modeling with Linear Functions — identifying the changing quantities in a situation, building a model from an intercept, from an input-output pair, or from a diagram, choosing a reasonable domain, and comparing two options by solving a system of linear models.
• Fitting Linear Models to Data — drawing and reading scatter plots, estimating a line of best fit by eye, interpolation and extrapolation, least squares regression, and using the correlation coefficient to judge how well a linear model describes the data.

This chapter is adapted from Precalculus 2e, Chapter 2: Linear Functions by Jay Abramson and OpenStax, © OpenStax, licensed under CC BY-NC-SA 4.0. Access the original for free at openstax.org. Each section page records its own adaptations.