Summary: The Coordinate Plane
Key Concepts
 Ordered Pair An ordered pair, [latex]\left(x,y\right)[/latex] gives the coordinates of a point in a rectangular coordinate system.[latex]\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}[/latex]
 Steps for Plotting an Ordered Pair (x, y) in the Coordinate Plane
 Determine the xcoordinate. Beginning at the origin, move horizontally, the direction of the xaxis, the distance given by the xcoordinate. If the xcoordinate is positive, move to the right; if the xcoordinate is negative, move to the left.
 Determine the ycoordinate. Beginning at the xcoordinate, move vertically, the direction of the yaxis, the distance given by the ycoordinate. If the ycoordinate is positive, move up; if the ycoordinate 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
Quadrant I Quadrant II Quadrant III Quadrant IV [latex](x,y)[/latex] [latex](x,y)[/latex] [latex](x,y)[/latex] [latex](x,y)[/latex] [latex](+,+)[/latex] [latex](−,+)[/latex] [latex](−,−)[/latex] [latex](+,−)[/latex]  Coordinates of Zero
 Points with a [latex]y[/latex]coordinate equal to [latex]0[/latex] are on the xaxis, and have coordinates [latex] (a, 0)[/latex].
 Points with a [latex]x[/latex]coordinate equal to [latex]0[/latex] are on the yaxis, and have coordinates [latex](0, b)[/latex].
 The point [latex](0, 0)[/latex] is called the origin. It is the point where the xaxis and yaxis 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 [latex]Ax+By=C[/latex], where [latex]A[/latex] and [latex]B[/latex] are not both zero, is called a linear equation in two variables.
 ordered pair
 An ordered pair [latex]\left(x,y\right)[/latex] gives the coordinates of a point in a rectangular coordinate system. The first number is the [latex]x[/latex] coordinate. The second number is the [latex]y[/latex] coordinate. [latex]\underset{x\text{coordinate},y\text{coordinate}}{\left(x,y\right)}[/latex]
 origin
 The point [latex]\left(0,0\right)[/latex] is called the origin. It is the point where the the point where the [latex]x[/latex] axis and [latex]y[/latex] axis intersect.
 quadrants
 The [latex]x[/latex] axis and [latex]y[/latex] 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 counterclockwise direction.
 solution to a linear equation in two variables
 An ordered pair [latex]\left(x,y\right)[/latex] is a solution to the linear equation [latex]Ax+By=C[/latex], if the equation is a true statement when the x and yvalues of the ordered pair are substituted into the equation.
 xaxis
 The xaxis is the horizontal axis in a rectangular coordinate system.
 yaxis
 The yaxis is the vertical axis on a rectangular coordinate system.
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 Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].