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.
