Coordinate Plane
Consists of a horizontal axis (typically labeled “x”) and a vertical axis (typically labeled “y”), crossing at the number zero on both axes.
Coordinate Pair, or Ordered Pair
The values of a point on a number line. The first number in the pair is the x-coordinate, which corresponds to the horizontal location of the point as measured by the x-axis. The second number in the pair is the y-coordinate, which corresponds to the vertical location of the point as measured by the y-axis.
Origin of a Coordinate Plane
The coordinate pair (0,0) represents the origin of a coordinate plane
Slope of a Line
The slope is defined as “rise over run,” or the distance the line runs vertically divided by the distance the line runs horizontally. The slope of any given line is constant over the length of that line. Given any two points on the line, take the difference between the y (or vertical) coordinates and divide that by the difference between the x (or horizontal) coordinates.
Types of Slopes
A line can have one of four types of slope: positive, negative, zero, or undefined. When viewing a line from left to right, the slope is positive if the line rises and negative if the line falls. If the line is perfectly horizontal, the slope is zero. If the line is perfectly vertical, the slope is undefined.
Intercept of a Line
A point where a line intersects a coordinate axis. If the line intersects the x-axis, the point is called the x-intercept, and the coordinate pair will take the form (x,0). If the line intersects the y-axis, the point is called the y-intercept, and the coordinate pair will take the form (0,y).
Slope-Intercept Equation
The slope-intercept equation is y=mx+b, where x and y represent the x and y coordinates of a particular point, m represents the slope of the line, and b represents the y-intercept.
Linear Equation
An equation that represents a straight line. An equation for a vertical line will take the form x = some constant number. An equation for a horizontal line will take the form y = some constant number. Equations for all other lines will include both an x term and a y term, and these two terms will be connected by either an addition symbol or a subtraction symbol. In all cases, a linear equation will never use terms such as x^2, √y, or xy.
Quadrants of a Coordinate Plane
The coordinate plane is divided into four quadrants. Quadrants are numbered beginning in the top right quadrant and moving counter-clockwise. Quadrant I contains points with a positive x-coordinate and a positive y-coordinate. Quadrant II contains points with a negative x-coordiante and a positive y-coordinate. Quadrant III contains points with a negative x-coordinate and a negative y-coordinate. Quadrant IV contains points with a positive x-coordinate and a negative y-coordinate.
Bisector
A line or line segment that cuts a line segment exactly in half.
Perpendicular Bisector
A line or line segment that cuts a line segment exactly in half and forms a 90º angle with that line.
Slopes of Perpendicular Lines
Two perpendicular lines have negative reciprocal slopes. For example, given two perpendicular lines and a slope of 2/3 for one of the lines, to find the slope of the second line, first take the reciprocal of the given slope (so 2/3 becomes 3/2) and then reverse the sign. In this case, the given slope was positive, so the sign becomes negative. The negative reciprocal slope of 2/3 is -3/2.
Parabola
The graph of a quadratic function. A quadratic function is an equation containing exponents or roots. For example, y = x^2 is a quadratic function.
