Ordered Pairs Part 1 Use the following equation to find an ordered pair (x, y) that will be a solution of: x + y = 10

Answer There are an infinite of solutions because x + y = 10 is a line that goes on forever!

COMMON CORE #11 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

WHAT IF………………………….. We change x + y = 10 to y = -x + 10 Would that keep our ordered pairs from working? Think about it anyway you can and write a brief explanation explaining your reasoning. It would change nothing as each ordered pair would still work. All that was changed was the x variable was moved across the = sign and it changed to a negative term.

Input and Output When you have y = -x + 10, Your x-values will be the input and y-values will be the output. This form is known as slope-intercept form.

Creating a Table of Ordered Pairs Lets use y = 4x to create a table of ordered pairs. We will use a two-column chart for our input/output values. You are allowed to pick any inputs you like, but -2 thru 2 is very common input numbers.

y = 4x x y -2 -1 1 2

y = 4x x y -2 -8 -1 -4 1 4 2 8

y = -2x x y -2 -1 1 2

y = -2x x y -2 4 -1 2 1 -4

A little harder example! Lets use the equation: y = 5x – 6 Why would this be a little harder?

y = 5x – 6 x y -2 -1 1 2

y = 5x – 6 x y -2 -16 -1 -11 -6 1 2 4

y = ½x + 4 x y -2 -1 1 2

y = ½x + 4 x y -2 3 -1 3.5 4 1 4.5 2 5

PRACTICE PROBLEMS (1) y = 2x (2) y = 4x - 1 Use -2 thru 2 for x-values #32 THINKING is required

APPLICATION Two ordered pairs of an equation are (6, 5) and (8, 5). What could the equation be? y = 0x + 5 or y = 5