This document discusses linear functions and how to graph them. It defines relations and functions, noting that a function has each input mapped to only one output. It states that a linear function forms a straight line on a graph. Methods for graphing linear functions include creating a table of x- and y-values by plugging inputs into the linear equation and plotting the points, or finding the x- and y-intercepts where the line crosses the axes.

1. Linear FunctionsAlgebra 2

2. RelationsA relation is a pairing of input and output values.RelationsA relation is a pairing of input and output values.

3. Can be represented graphically by a set of ordered pairs (x, y).FunctionsA relation is a function when each input value has one and only one output value. Example 1DomainRangeVertical Line Test

4. Linear FunctionsA linear function makes a line on a graph.Linear FunctionsA linear function makes a line on a graph.

5. A solution to a linear function is a point on the line.Example 2

6. GraphingThe graph of a function is the set of ALL the points (x, y) that satisfy the equation.GraphingThe graph of a function is the set of ALL the points (x, y) that satisfy the equation.

7. For a linear function, all these points together create a line.GraphingOne way to graph a linear function is to create a table of values.GraphingOne way to graph a linear function is to create a table of values.Solve the equation for y.

8. GraphingOne way to graph a linear function is to create a table of values.Solve the equation for y.Choose a few x-values to plug in and find the corresponding y-values.

9. GraphingOne way to graph a linear function is to create a table of values.Solve the equation for y.Choose a few x-values to plug in and find the corresponding y-values.Plot these points.

10. GraphingOne way to graph a linear function is to create a table of values.Solve the equation for y.Choose a few x-values to plug in and find the corresponding y-values.Plot these points.Connect with a straight line.

11. Example 3

12. InterceptsAnother way to graph a function is to find its x- and y-intercepts.

13. The intercept is where it crosses the axes.InterceptsFor the x-intercept, y is …?

14. For the y-intercept, xis …?