Warm-Up1) Graph -7 on a horizontal number line.2) Graph 4 on a vertical number line.

Chapter 5 Graphing Linear Equations

5.1 The Cartesian plane

Objective: Students will be able to graph an ordered pair and label parts of the Cartesian plane.I.Parts of the Cartesian PlaneThe Cartesian plane is made up of two number lines, one vertical number line and one horizontal line. These lines intersect at zero for each number line.Each number line is called an axis. Each axis is assigned a variable. Normally y is assigned for the vertical axis and x is assigned for the horizontal axis.Note: The plural of axis is axes.

The intersection of the two number lines is called the origin.The positive direction is always up and to the right.Notice that the white part is broken into 4 parts, these parts are called Quadrants.To number the quadrants,start in the upper right quad-rant and go counter-clockwise.

II. Plotting points on the Cartesian PlaneEach point is named by two numbers, these are called ordered pairs. i.e. (-3, 7)These numbers determine where on the Cartesian

plane the point lies.The first number is how far the point is from the origin in the horizontal direction.The second number is how far the point is from the

origin in the vertical direction.So to plot the point (-3, 7) you start at the origin and

go left 3 units and up 7 units.Note (0, 0) is the origin.

PracticePlot the following points on graph paper.A – (4, 1)B – (0, 5)C – (-2, 5)D – (5, -3)E – (-6, -1)

Warm-UpPlot the following points and state what quadrant

they are located in.1) (-3, 5)2) (4, -3)3) (-2, -6)

Cont of 5.1 The Cartesian plane

III. Relation vs FunctionA relation is any set of ordered pairs.

Examples: {(2, 4), (3,9), (-2,6)} {(Ohio, Columbus), (California, Sacramento), (Georgia, Atlanta)}

{(dog, puppy), (cat, kitten)A mapping diagram shows which coordinates are related.The domain is the set of first coordinates of a relation.The range is the set of second coordinates of a relation.

Practice1) Make a mapping diagram for the following relation:{(2, 4), (3,9), (-2,6), (7,4)}2) What is the domain of the following relation?{(2, 4), (3,9), (-2,6), (7,4)}3) What is the range of the following relation?{(2, 4), (3,9), (-2,6), (7,4)}

III. Relation vs FunctionA function is a relation whose elements in the domain are mapped to one and only one element in the range.

Homework 5.1 Due Thursday