## Key Concepts

- We can locate, or plot, points in the Cartesian coordinate system using ordered pairs, which are defined as displacement from the
*x-*axis and displacement from the*y-*axis. - An equation can be graphed in the plane by creating a table of values and plotting points.
- Using a graphing calculator or a computer program makes graphing equations faster and more accurate. Equations usually have to be entered in the form
*y=*_____. - Finding the
*x-*and*y-*intercepts can define the graph of a line. These are the points where the graph crosses the axes. - The distance formula is derived from the Pythagorean Theorem and is used to find the length of a line segment.
- The midpoint formula provides a method of finding the coordinates of the midpoint dividing the sum of the
*x*-coordinates and the sum of the*y*-coordinates of the endpoints by 2.

## Glossary

**Cartesian coordinate system** a grid system designed with perpendicular axes invented by RenĂ© Descartes

**distance formula** a formula that can be used to find the length of a line segment if the endpoints are known

**equation in two variables** a mathematical statement, typically written in *x *and *y*, in which two expressions are equal

**graph in two variables** the graph of an equation in two variables, which is always shown in two variables in the two-dimensional plane

**intercepts** the points at which the graph of an equation crosses the *x*-axis and the *y*-axis

**midpoint formula** a formula to find the point that divides a line segment into two parts of equal length

**ordered pair** a pair of numbers indicating horizontal displacement and vertical displacement from the origin; also known as a coordinate pair, [latex]\left(x,y\right)[/latex]

**origin** the point where the two axes cross in the center of the plane, described by the ordered pair [latex]\left(0,0\right)[/latex]

**quadrant** one quarter of the coordinate plane, created when the axes divide the plane into four sections

** x-axis** the common name of the horizontal axis on a coordinate plane; a number line increasing from left to right

** x-coordinate** the first coordinate of an ordered pair, representing the horizontal displacement and direction from the origin

** x-intercept** the point where a graph intersects the

*x-*axis; an ordered pair with a

*y*-coordinate of zero

** y-axis** the common name of the vertical axis on a coordinate plane; a number line increasing from bottom to top

** y-coordinate** the second coordinate of an ordered pair, representing the vertical displacement and direction from the origin

** y-intercept** a point where a graph intercepts the

*y-*axis; an ordered pair with an

*x*-coordinate of zero