Algebra 1 ~ Chapter 4.1 The Coordinate Plane

4-1: The Coordinate Plane -Where we graph points. -A grid created by two intersecting lines we call Axes. -Each axis is like a number line. -One horizontal line. -One vertical line. -These Axes divide the coordinate plane into 4 quadrants. Y-Axis (Vertical Line) II I X-Axis (Horizontal Line) III IV

Points Points are called Ordered Pairs. Ordered Pairs are written in the form of (x,y) (x-coordinate, y-coordinate) (Direction along the x-axis, Direction along the y-axis) Y X

Origin (0,0) Origin: (0 along the x-axis,0 along the y-axis)

Signs of Points Ordered Pairs have unique signs depending upon the quadrant they appear in… Quadrant I Quadrant II Quadrant III Quadrant IV (– ,+) (+,+) (–, –) (+, –)

Find the Ordered Pair: Fill In the Table Point X-Coord. Y-Coord. Ordered Pair Quadrant .A .B .C 1 2 (1,2) I .A 2 -1 (2, –1) IV –1 –2 III (–1, –2) .B .C

Graphing Ordered Pairs How to draw a point on the coordinate plane that corresponds to that ordered pair. 1)Start at the origin 2)Move x units horizontally first 3)Then move y units vertically (x,y)

Practice Graphing Points B: (0, –3) C: (–2, 0) D: (–1, –2) E: (4, –1) F: (–3, 3) .F .D .A .E .B .C

Chapter 4.3 Relations

In Chapter 1, we learned that a set of ordered pairs (coordinates) is called a relation. A relation can be represented by a set of ordered pairs, a table, a graph or a mapping diagram. A mapping diagram will illustrate how each element of the domain (the x’s) is paired with an element in the range (the y’s).

Representing Relations

Write all x-values under “x” and all y-values under “y”. Express the relation {(2, 3), (4, 7), (6, 8)} as a table, as a graph, and as a mapping diagram. x y Table 2 4 6 3 7 8 Write all x-values under “x” and all y-values under “y”.

Use the x- and y-values to plot the ordered pairs. Example 1 Continued Express the relation {(2, 3), (4, 7), (6, 8)} as a table, as a graph, and as a mapping diagram. Graph Use the x- and y-values to plot the ordered pairs.

Example 1 Continued Express the relation {(2, 3), (4, 7), (6, 8)} as a table, as a graph, and as a mapping diagram. Mapping Diagram x y Write all x-values under “x” and all y-values under “y”. Draw an arrow from each x-value to its corresponding y-value. 2 6 4 3 8 7

Remember that the domain of a relation is the set of first coordinates (or x-values) of the ordered pairs. The range of a relation is the set of second coordinates (or y-values) of the ordered pairs.

Example 2 – Use the mapping diagram below to identify the domain and range. Notice that 2 of the 5 coordinates have a y-value of 4, but we only list the 4 once on the “range” list. Also, notice that we listed the numbers in order from least to greatest.

Example 3 – Write the four ordered pairs represented in the mapping diagram. 1 2 6 5 –4 –1 {(6, -1), (5, 0), (2, -4), (1, 0)}

Example 4 – Identify the ordered pairs represented by the table. x y 1 4 8 {(1, 1), (4, 4), (8, 1)}

Page 206 ~ Bald Eagles Example The data is given in a table and then we can use that information to make a graph. The x-values (domain) are years. The y-values (range) are the # of eagles.

Inverse Relations The inverse of any relation is obtained by switching the coordinates in each ordered pair. For example, ordered pair (a, b) has the inverse ordered pair (b, a).

Relation - Inverse Relation (2, 5) (-3, 2) (6, 7) (5, -1) Inverse (5, 2) (2, -3) (7, 6) (-1, 5) Notice that the domain of a relation becomes the range of the inverse and the range of a relation becomes the domain of the inverse.

Lesson Review 1. Express the relation {(–2, 5), (–1, 4), (1, 3), (2, 4)} as a table, as a graph, and as a mapping diagram.

Assignment Skills Worksheet 4-1 / 4-3 (Front & Back)