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Boundless Algebra
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Chapter 5

Linear Functions

Book Version 13
By Boundless
Boundless Algebra
Algebra
by Boundless
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Section 1
Introduction to Linear Functions
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What is a Linear Function?

Linear functions are algebraic equations whose graphs are straight lines with unique values for their slope and y-intercepts.

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Slope

Slope describes the direction and steepness of a line, and can be calculated given two points on the line.

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Direct and Inverse Variation

Two variables in direct variation have a linear relationship, while variables in inverse variation do not.

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Zeroes of Linear Functions

A zero, or $x$-intercept, is the point at which a linear function's value will equal zero.

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Slope-Intercept Equations

The slope-intercept form of a line summarizes the information necessary to quickly construct its graph.

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Point-Slope Equations

The point-slope equation is another way to represent a line; only the slope and a single point are needed.

Linear Equations in Standard Form

Any linear equation can be written in standard form, which makes it easy to calculate the zero, or $x$-intercept, of the equation.

Section 2
Working With Lines
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The Distance Formula and Midpoints of Segments

The distance and the midpoint formulas give us the tools to find important information about two points.

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Parallel and Perpendicular Lines

Parallel lines never intersect; perpendicular lines intersect at right angles.

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Linear Inequalities

A linear inequality is an expression that is designated as less than, greater than, less than or equal to, or greater than or equal to.

Section 3
Applications of Linear Functions
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Rates of Change

Linear functions apply to real world problems that involve a constant rate.

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Linear Mathematical Models

Linear mathematical models describe real world applications with lines.

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Fitting a Curve

Curve fitting with a line attempts to draw a line so that it "best fits" all of the data.

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Boundless Algebra by Boundless
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Functions
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Chapter 5
Linear Functions
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  • Working With Lines
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Chapter 6
Quadratic Functions and Factoring
  • Introduction to Quadratic Functions
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