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
Sunday, February 1, 2009
Math 6 H Periods 1, 6 & 7
Graphs of Ordered Pairs 11-8
The location of a desk in a classroom can be described as “ second row, third desk” If we write (2, 3) to represent this location, the order of the numbers is important since (3, 2) would represent “third row, second desk) a pair of numbers whose order is important is called an ordered pair. Remember when you first walked into our classroom on the very first day—You had to find your seat – and it was an ordered pair!!
We graph a number as a point on a number line. We graph an ordered pair of numbers as a point on a plane marked with two perpendicular number lines called axes. The first number of an ordered pair is associated with the horizontal number line—called the x- axis and the second number with the vertical number line, called the y axis. The axes meet in a point, called the origin (0, 0).
Open your books to Page 389 to review - we are looking at the top graph on that page. To locate the ordered pair (3,2) start at the origin—where is that?—go 3 units to the right and then 2 units up. The numbers 3 and 2 are the coordinates of the graph (3, 2) the plane itself is called a coordinate plane.
Remember (x, y) it is x first, then y. It is Horizontal first, then Vertical, Across and then Up/Down its easy to remember… each is alphabetically in order..
The location of a desk in a classroom can be described as “ second row, third desk” If we write (2, 3) to represent this location, the order of the numbers is important since (3, 2) would represent “third row, second desk) a pair of numbers whose order is important is called an ordered pair. Remember when you first walked into our classroom on the very first day—You had to find your seat – and it was an ordered pair!!
We graph a number as a point on a number line. We graph an ordered pair of numbers as a point on a plane marked with two perpendicular number lines called axes. The first number of an ordered pair is associated with the horizontal number line—called the x- axis and the second number with the vertical number line, called the y axis. The axes meet in a point, called the origin (0, 0).
Open your books to Page 389 to review - we are looking at the top graph on that page. To locate the ordered pair (3,2) start at the origin—where is that?—go 3 units to the right and then 2 units up. The numbers 3 and 2 are the coordinates of the graph (3, 2) the plane itself is called a coordinate plane.
Remember (x, y) it is x first, then y. It is Horizontal first, then Vertical, Across and then Up/Down its easy to remember… each is alphabetically in order..
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