How To Find Ordered Pairs On A Graph

Ordered Pairs

An ordered pair is a pair of numbers in a specific society. For example, (one, ii) and (- 4, 12) are ordered pairs. The society of the two numbers is important: (i, 2) is not equivalent to (2, 1) -- (i, 2)≠(2, one).

Using Ordered Pairs to Represent Variables

Ordered pairs are often used to represent two variables. When we write (10, y) = (7, - 2), nosotros mean ten = vii and y = - 2. The number which corresponds to the value of 10 is called the x-coordinate and the number which corresponds to the value of y is called the y-coordinate.

Example 1. If (x, y) = (- 1, four), what is the value of 310 + 2y - 4 ?
3x + 2y - iv = 3(- 1) + 2(4) - 4 = - 3 + 8 - iv = 1

Instance ii. Which of the following ordered pairs (10, y) are solutions to the equation - 6 = 1 ? {(4, i),(five, ii),(- 3, 1),(- 3, -1),(1, 4)}
(x, y) = (4, 1): -6 = - half dozen = seven - six = one. Solution.
(x, y) = (5, 2): -6 = -6 = -vi = - ≠1. Not a solution.
(x, y) = (- 3, 1): -six = -six = - seven - 6 = - thirteen≠1. Not a solution.
(x, y) = (- 3, - i): -6 = - six = seven - vi = 1. Solution.
(x, y) = (1, 4): -6 = -6 = -6 = - ≠1. Not a solution.
Thus, {(4, 1),(- 3, -1)} are solutions to - 6 = 1.

Graphing Ordered Pairs

Nosotros take graphed values on the number line in pre- algebra and in earlier chapters of algebra. Yet, we can only graph points of one variable on the number line; thus, nosotros need a 2-dimensional (ii variable) fashion of representing points -- the xy-graph:

The horizontal centrality, called the ten-axis, represents values of ten , and the vertical axis, chosen the y-centrality, represents values of y . From now on, the give-and-take "graph" will refer to the xy -graph, unless specified otherwise.

To graph a point on the xy -graph, first find the x -coordinate on the x -axis. Then motility up on the graph the number of spaces which is equal to the y -coordinate (or motility down if the y -coordinate is negative). For example, to graph (two, iii), find two on the x -centrality. Then move upwards 3 spaces. To graph (- 2, i), discover -2 on the x -axis, then motility upward i space. To graph (1.v, - i), discover 1.5 on the x -axis, then move down one space: