## Key Concepts

Contents

**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.

- Points with a

## 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.

### 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.