Coordinates and Graphs of Lines
Solutions to Equations in Two Variables
To find ordered pairs that satisfy the equation, we first solve (if possible)
for y in terms of x. Then we construct a T Table that consists of two
columns. The first represents the x coordinate and the second column
represents the y coordinate.
Now we construct a table by plugging in several values of x and find y:
x = 0: y = 2(0) - 4 = -4
x = 1: y = 2(1) - 4 = -2
x = 2: y = 2(2) - 4 = 0
x = 3: y = 2(3) - 4 = 2
x = -1: y = 2(-1) - 4 = -6
We create our table:
This is called a T-table.
The Coordinate Axes and Graphing
Just as we draw a number line to represent real numbers, we can also represent ordered pairs. We draw two number lines that intersect each other at right angles. We call the plane that the two number lines lie in the xy-plane. We call the horizontal line the x-axis and the vertical line the y-axis. We let the right of the x-axis represent positive x values, while the top of the y-axis represents positive y values. The intersection point is where x = 0 and y = 0 is called the origin. The top right part of the plane is called Quadrant I. The top left part of the plane is called Quadrant II. The bottom left part of the plane is called Quadrant III. The bottom right part of the plane is called Quadrant IV. To represent an ordered pair (x,y) on the xy-plane, we walk x units to the right and y units upward. Below are the points (1,2), (-1,1), (-2,-1), and (2,-1) plotted on the xy-plane.
Horizontal and Vertical Lines
Horizontal and vertical lines have special equation that we describe below.