Key Concepts

• 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 x-axis, and have coordinates [latex] (a, 0)[/latex].
  • Points with a [latex]x[/latex]-coordinate equal to [latex]0[/latex] are on the y-axis, and have coordinates [latex](0, b)[/latex].
  • The point [latex](0, 0)[/latex] is called the origin. It is the point where the x-axis and y-axis intersect.

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.

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 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.