# Algebra 2 Algebra 2 Chapter 2: Linear Relations and Functions Section 2.1 Relations and Functions Objectives Analyze and graph relations.

Find functional values. Vocabulary Ordered Pair: A pair of coordinates, written in the form (x, y), used to locate any point on a coordinate plane.

Cartesian Coordinate Plane: composed of the x-axis (horizontal) and y-axis (vertical), which meet at the origin (0, 0) and divide the plane into four quandrants. Relation; Domain; Range

Relation: is a set of ordered pairs. Domain (of a relation): the set of all first coordinates (xcoordinates) from the ordered pairs. Range (of a relation): the set of all second coordinates (ycoordinates) from the order pairs.

Relation: { (12, 28), (15, 30), (8, 20), (12, 20), (20, 50)} Domain: {8, 12, 15, 20}

Range: {20, 28, 30, 50} Function

A function is a special type of relation. Each element of the domain is paired with exactly one element of the range. A mapping shows how the members are paired. An example is shown to the right. The example to the right is a function; each element of the domain is paired with exactly one element of the domain. This is called a one-to-one

function. Functions can be represented as When speaking, we say F of x or G of x. Relation: {(12, 28), (15, 30), (8, 20)} Domain Range

12 28 15 30 8 20

Function or not? Domain Domain Range Range -3

1 -1 0 2 1 3

2 4 4 5 Function Function Domain

Range -3 0 1 1 5

6 NOT a Function Relations: Discrete or Continuous? Discrete Discrete graphs contain a set of points not connected. Continuous Continuous graphs contain a smooth line

or curve. Note: You can draw the graph of a continuous relation Without lifting you pencil from the paper. Vertical Line Test If no vertical line intersects a graph in more than one point, the graph represents a function.

If some vertical line intersects a graph in two or more points, the graph DOES NOT represent a function. Graphing Relations See examples on pages 60 and 61 in your textbook.

When graphing, create a table of values. Evaluate a function Given , find each value. a.

f(-3) b. f(3z) 11 HOMEWORK..A#2.1 Assigned on Friday, 9/20/13

Due on Monday, 9/23/13 Pages 62-63 [#13-20 all, 24, 34, 36, 40] Section 2.2 Linear Equations Section Objectives

Identify linear equations and functions. Write linear equations in standard form and graph them. Identify Linear Equations and Functions A linear equation has no operations other than addition, subtraction, and multiplication

of a variable by a constant. The variables may not be multiplied together or appear in a denominator. It does not contain variables with exponents other than 1. The graph of a linear equation is always a line. Linear Equations NOT Linear Equations

Identify Linear Equations State whether each function is a linear function. Explain. Standard Form The standard form of a linear equation is

where A, B, and C are integers whose greatest common factor is 1, , and A and B are not both zero. Write each equation in standard form. Identify A, B, and C. Graphing with Intercepts X-Intercept: the x-coordinate of the point at which it crosses the xaxis.

y=0 Y-Intercept: the y-coordinate of the point at which it crosses the yaxis. x=0 Find the x-intercept and y-intercept of the graph of Then graph the equation. Find the x-intercept and y-intercept of the graph of Then graph the equation.

HOMEWORK..A#2.2 Assigned on Monday, 9/23/13 Due on Tuesday, 9/24/13

Page 107 [#16-22 all] Section 2.3 Slope Objectives for Section 2.3 Find and use the slope of a line.

Graph parallel and perpendicular lines. Vocabulary A rate of change measures how much a quantity changes, on average, relative to the change in another quantity, often time. The slope (m) of a line is the ratio of the change in y-coordinates to the corresponding change in x-coordinates.

The slope m of the line passing through and is given by , where Find the slope of the line that passes through (-1, 4) and (1, -2). Then graph the line. Find the slope of the line that passes through (1, -3) and (3, 5). Then graph the line. Slope tells the direction in which it rises or falls.

Negative Slope Zero slope Family of graphs A family of graphs is a group of graphs that displays one or more similar characteristics.

The parent graph is the simplest of the graphs in a family. Parent: y = x Family: y = 3x + 2 y=x+2 Parallel Lines In a plane, nonvertical lines with the same slope are parallel. All vertical lines are parallel.

Graph the line through (-1, 3) that is parallel to the line with equation . Graph the line through (-2, 4) that is parallel to the line with equation 3. Perpendicular Lines Two lines are perpendicular if

the product of their slopes = . When you have two perpendicular lines, their slopes are opposite reciprocals of each other. Slope of line AB: C(-3,2) A(2,1) Slope of line CD: D(1,-4)

B(-4,-3) Graph the line through (-3, 1) that is perpendicular to the line with equation Graph the line through (-6, 2) that is perpendicular to the line with equation HOMEWORK..A#2.3 Assigned on

Due on Page 108 [#23-29 all] Section 2.4 Writing Linear Equations

Objectives After this section, you will be able to Write an equation of a line given the slope and a point on the line. Write an equation of a line parallel or perpendicular to a given line. Slope-Intercept Form of a Linear

Equation = + slope y-intercept Write an Equation Given Slope and a Point

Write an equation in slope-intercept form for the lines that has a slope of and passes through the point (3, 2). Practice Write and equation in slope-intercept form for the line that has a slope of and passes through Graph an Equation in SlopeIntercept Form

Graph the following equations: Point-Slope Form of a Linear Equation Slope 1=( 1 ) Given point Write an Equation Given Two Points

What is the equation of the line through Procedure: 1. Find the slope. 2. Write an equation using slope and one of the given points. Write an Equation of a Perpendicular

Line Write an equation for the line that passes through (3, 7) and is perpendicular to the line whose equation is . HOMEWORK..A#2.4 Assigned on Thursday 9/26/13

Due on Friday 9/27/13 Page 108 [#30-34 all] Section 2.5 Statistics: Using Scatter Plots Objectives After this section, you will be able to

Draw scatter plots. Find and use prediction equations. Vocabulary

Bivariate Data: Scatter Plot: Speed (mph) Calories 5

508 6 636 7 731 8

858 Scatter Plot Correlations Prediction Equations Line of Fit:

Prediction Equation: To find a line of fit and prediction equation: Find and Use a Prediction Equation HOUSING: The table below shows the median selling price of new, privately-owned, one-family houses for some recent years. Year

1994 1996 1998 2000 2002 2004

Price (\$1000) 130.0 140.0 152.5 169.0 187.6

219.6 Draw a Scatter Plot and a line of fit for the data. How well does the line fit the data? 250 Price (\$1000) 230 210 190

170 150 130 110 0 2 4 6

8 10 Years since 1994 Year 1994 1996

1998 2000 2002 2004 Price (\$1000) 130.0

140.0 152.5 169.0 187.6 219.6 Find a prediction equation. What do

the slope and y-intercept indicate? Predict the median price in 2014. How accurate does the prediction appear to be? PRACTICE The table shows the mean selling price of new, privately owned onefamily homes for some recent years. Draw a scatter plot and line of fit for the data. Then find a prediction equation and predict the mean price in 2014.

Year 1994 1996 1998 2000 2002

2004 Price (\$1000) 154.5 166.4 181.9

207.0 228.7 273.5 1994 1996 1998

2000 2002 2004 Price (\$1000) 154.5 166.4

181.9 207.0 228.7 273.5 Price (\$1000) Year

Years since 1994 Practice workspace HOMEWORK..A#2.5 Assigned on Monday 9/30/13

Due on Tuesday 10/1/13 Page 89 [#3-9 all]