Boundary Line

The line that divides a coordinate plane into two halves. To find it, we graph the inequality like it's an equation, using a dotted line for strict inequalities (< or >), or a solid line for non-strict inequalities (≤ or ≥). The solution of a linear inequality will be the entire area on one side of the boundary line. Try to respect other people's boundary lines, or they might get testy.

Coordinate Plane

The surface on which a set of axes is drawn. In other words, the plane for the graph.

Dependent Variable

This is the variable that depends on how the independent variable is feeling at the moment. It's a tough job, but someone's got to do it. In a function, the dependent variable is y.

Domain

The possible inputs (x-values) for a given function. Like a list of all the fuels that can go in your car. (Orange juice is not on that list. Boy did we learn that the hard way.)

Function

A relation where each domain value has one and only one range value. Functions must pass the vertical line test. See? You aren't the only one that has to pass tests.

Independent Variable

This is the variable that does whatever it wants. It can be whatever it wants, and it's not changing for anyone. Well, it'll change for you if you ask it nicely. In a function, the independent variable is x.

Intercept

A point on a graph where a line or plane crosses one of the axes.

Ordered Pair

An x-coordinate and a y-coordinate expressed in the form (x, y).

Origin

The point (0, 0) on the x-y graph. In 3D space, it's (0, 0, 0). For any additional dimensions, just add more zeros.

Piecewise Function

A function whose definition changes depending on the input.

Parallel Lines

Lines that will never intersect, because they share the same slope.

Perpendicular Lines

Two lines that intersect at a right angle. Actually, they make four right angles.

Point-slope Form

Linear equation of the form y – y₁ = m(x – x₁), where m is the slope of the line, and (x₁, y₁) is a point that falls on the line. All we need is some music, and we have a party.

Range

The set of all possible outputs (y-values) of the function.

Slope

The steepness of a line, calculated as rise over run; think skiing (the bunny slope is less steep than the triple black diamond).

Slope-Intercept Form

The equation of a linear function in the form y = mx + b, where m is the slope and b is the y-intercept of the line. Some mathematicians play favorites and like this form the best.

Standard Form

Another way to write the equation of a line. It's y = Ax + By = C, where A, B, and C are all real numbers, and A and B cannot both be 0 at the same time.

Step Function

A piecewise function that looks like a set of stairs.

Two-points Method

A way to find the equation of a line with only two points. First we use both points to track down the slope, then pick one of the points and plug it and the slope into the point-slope formula. A technique for master detectives.

Vertex

The sharp, pointy bit of an absolute value graph.