Mathematics » Introducing Graphs » Use the Rectangular Coordinate System

Key Concepts

Key Concepts

  • Sign Patterns of the Quadrants
    Quadrant IQuadrant IIQuadrant IIIQuadrant IV
    (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.

Glossary

linear equation

An equation of the form \(Ax+By=C,\) where \(A\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}B\) 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.

quadrants

The \(x\)-axis and \(y\)-axis divide a rectangular coordinate system into four areas, called quadrants.

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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