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# Summary: The Coordinate Plane

## Key Concepts

• Ordered Pair  An ordered pair, $\left(x,y\right)$ gives the coordinates of a point in a rectangular coordinate system.$\begin{array}{c}\text{The first number is the }x\text{-coordinate}.\hfill \\ \text{The second number is the }y\text{-coordinate}.\hfill \end{array}$
• Steps for Plotting an Ordered Pair (x, y) in the Coordinate Plane
• Determine the x-coordinate. Beginning at the origin, move horizontally, the direction of the x-axis, the distance given by the x-coordinate. If the x-coordinate is positive, move to the right; if the x-coordinate is negative, move to the left.
• Determine the y-coordinate. Beginning at the x-coordinate, move vertically, the direction of the y-axis, the distance given by the y-coordinate. If the y-coordinate is positive, move up; if the y-coordinate is negative, move down.
• Draw a point at the ending location. Label the point with the ordered pair.
• An ordered pair is represented by a single point on the graph.
• Sign Patterns of the Quadrants
$(x,y)$ $(x,y)$ $(x,y)$ $(x,y)$
$(+,+)$ $(−,+)$ $(−,−)$ $(+,−)$
• Coordinates of Zero
• Points with a $y$-coordinate equal to $0$ are on the x-axis, and have coordinates $(a, 0)$.
• Points with a $x$-coordinate equal to $0$ are on the y-axis, and have coordinates $(0, b)$.
• The point $(0, 0)$ is called the origin. It is the point where the x-axis and y-axis intersect.
• Identifying Solutions  To find out whether an ordered pair is a solution of a linear equation, you can do the following:

• Graph the linear equation, and graph the ordered pair. If the ordered pair appears to be on the graph of a line, then it is a possible solution of the linear equation. If the ordered pair does not lie on the graph of a line, then it is not a solution.
• Substitute the (x, y) values into the equation. If the equation yields a true statement, then the ordered pair is a solution of the linear equation. If the ordered pair does not yield a true statement then it is not a solution.

## Glossary

linear equation
An equation of the form $Ax+By=C$, where $A$ and $B$ are not both zero, is called a linear equation in two variables.
ordered pair
An ordered pair $\left(x,y\right)$ gives the coordinates of a point in a rectangular coordinate system. The first number is the $x$ -coordinate. The second number is the $y$ -coordinate. $\underset{x\text{-coordinate},y\text{-coordinate}}{\left(x,y\right)}$
origin
The point $\left(0,0\right)$ is called the origin. It is the point where the the point where the $x$ -axis and $y$ -axis intersect.
The $x$ -axis and $y$ -axis divide a rectangular coordinate system into four areas, called quadrants.  The quadrants are labeled with the Roman Numerals I, II, III, IV going around the coordinate system in a counter-clockwise direction.
solution to a linear equation in two variables
An ordered pair $\left(x,y\right)$ is a solution to the linear equation $Ax+By=C$, if the equation is a true statement when the x- and y-values of the ordered pair are substituted into the equation.
x-axis
The x-axis is the horizontal axis in a rectangular coordinate system.
y-axis
The y-axis is the vertical axis on a rectangular coordinate system.

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