# PA Chapter 8 Linear Functions

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Linear Functions

### Relations

Any set of points.

### Domain

The set of x-values.

### Range

The set of y-values.

### Input

Each domain value.

### Output

Each range value.

### Function

A relation with no repeating x-values such that there is exactly one output for each input.

### Mapping Diagram

Lists the inputs and outputs in order drawing arrows from the inputs to their outputs.

### Vertical Line Test

A visual test on a graph to determine if the relation is a function. If this line passes through more than one point, then it is not a function.

x = c

y = c

ax + by = c

y = mx + b

### x-intercept

(x,0); The point which crosses the x-axis.

### y-intercept

(0,y); The point which crosses the y-axis.

### Increasing

A graph that rises from left to right.

### Decreasing

A graph that falls from left to right.

### Linear Function Graph

A function whose graph is a nonvertical line.

### Nonlinear Function Graph

A function whose graph is not a line.

### Slope

Rise/Run; Difference of the y-coordinates/Difference of the x-coordinates.

### Positive Slope

An increasing line has this type of slope.

### Negative Slope

A decreasing line has this type of slope.

### Zero slope

A horizontal line has this type of slope.

### Undefined Slope

A vertical line has this type of slope.

### Same Slope

Parallel lines have this type of slope.

### Opposite Reciprocal Slope

Perpendicular lines have this type of slope.

### y-intercept

If a function is in the format y = mx + b, the b is the ___.

### Direct Variation

Two points are in _____ if they relate to each other as y=kx.

### Function Notation

Written as f(x), is read as "f of x", and represents the value of y given a value of x.

### Systems of Linear Equations

Two or more linear equations.

### Coordinate Point

A solution of a system is written as a _______ representing where the two lines cross.

Example:

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