Purpose: To graph ordered pairs and linear equations in two variables. Homework: p odd.

Definitions Consider two number lines, one horizontal and one vertical. The two lines are perpendicular to each other at their zero points. These number lines make up the axes of a coordinate system. The horizontal line is called the x-axis, which is positive to the right and negative to the left. The vertical line is called the y-axis, which is positive going up and negative going down. The intersection of both x-axis and y-axis at there zero points is called the origin. The intersection of the axes also divides the plane into four regions called quadrants. The quadrants are numbered counterclockwise form one to four.

Ordered Pairs

Definitions (cont.) Ordered Pairs are pairs of real numbers that describe a point in the coordinate system. The ordered pair describes a point in the plane by its x and y coordinates. (x,y) is a point in the plane. The first number describes the distance in the x-axis; also called the abscissa. The second number describes the distance in y-axis, also called the ordinate. The point (0,0) is the origin of the graph. Points are named by using capital letters, and point O often refers to the origin (0,0).

In the first quadrant, both the x and y-coordinate are positive. In the second quadrant, the x-coordinate is negative and the y-coordinate is positive. In the third quadrant, both the x and y- coordinate are negative. In the fourth quadrant, the x-coordinate is positive and the y-coordinate is negative.

Standard Form ax + by = c is a linear equation said to be in standard form. a, b, and c are nonzero real numbers. y = mx + b is a linear equation NOT in standard form xy = 6 and x² + xy are NON-Linear equations.

Vertical Lines

Horizontal Lines