## Key Concepts

• Sign Patterns of the Quadrants
Quadrant I Quadrant II Quadrant III Quadrant 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 $A$ 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.
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.