## 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 by 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 René Descartes

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

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

**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

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