Math 6 H Periods 1, 6 & 7

Graphs of Equations 11-9

An equation in two variables can produce many ordered pairs.
y = 2 – x

If we give x the value of 3, for example a corresponding value of y is determined.

y = 2- 3
y = -1
We describe this correspondence by the ordered pair (3, -1). We can created a table that shows several other ordered pairs produced by y = 2 –x

x ---> 2 - x = y ---> Ordered pair (x, y)
-1 ---> 2- -1 = 3 ---> (-1, 3)
0 ---> 2 – 0 = 2---> (0, 2)
1 ---> 2 - 1 = 1---> (1, 1)
2 ---> 2 - 2 = 0---> (2, 0)
3 ---> 2 - 3 = -1---> (3, -1)
4 ---> 2 - 4 = -2---> (4, -2)

Let’s plot those ordered pairs. The diagram suggests that if we were able to graph all of the ordered pairs produced by y = 2-x we would obtain a line. This line is the graph of the equation y = 2-x



Graph the equation y = 2x – 3

First make a table of ordered pairs and then graph the ordered pairs on a coordinate plane.

x---> 2x-3 = y---> ordered pair
-1---> 2(-1) – 3 = -5---> (-1, -5)
0---> 2(0) – 3 = -3---> (0, -3)
1---> 2(1) – 3 = -1---> (1, -1)
2---> 2(2) – 3 = 1---> (2, 1)



In the set of ordered pairs, for each value of x there is exactly one value of y. A set of ordered pairs such as this, in which no two ordered pairs have the same first component is called a function. For example, we can say that y = 2x -3 defines y as a function of x