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

(x, y)

$\left(x,y\right)$ gives the coordinates of a point in a rectangular coordinate system. The first number is the

x

$x$ -coordinate. The second number is the

y

$y$ -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.