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 René 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