Download Ordered Pairs and Linear Equations

Ordered Pairs and Linear Equations
Linear Equation: the equation of a line.
It may have one or two variables. 2x + 3y = 6, y = 5, and x = 2 are all equations of lines.
Solutions of linear equations: all of the points whose coordinates (x, y) make the
equation a true statement. A line contains an infinite number of points. Therefore, there
are an infinite number of ordered pairs that “work” in the equation of a line.
If the directions say …
Just do this …
Determine if a point is on a line…
Plug the coordinates of the point into the
equation of the line and see if you get a
true statement.
Or determine whether an ordered pair is a
solution to an equation…
Example: Determine if (2, 1) is on the line x + y = 3. Since 2 + 1 = 3, it is on the line.
Completing ordered pair solutions: Plug the value that you know into the equation
and solve for the missing one.
Note: (3, ) means x = 3 and you need to find y
( , 5) means y = 5 and you need to find x
y = 3x + 8
Find the missing coordinate:
(2, )
y = 3(2) + 8
y = 6 + 8 = 14
Point is (2, 14)
y = 3x + 8
Find the missing coordinate:
20 = 3x + 8
Subtract 8 from each side
12 = 3x
Divide by 3
4=x
Point is (4, 20)
( , 20)