Mathematics » Introducing Graphs » Use the Rectangular Coordinate System

# Key Concepts

## Key Concepts

• Sign Patterns of the Quadrants
(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.

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.