Glossary
Every term you'll meet across Plane & Point — the lessons, the calculator, the solver, and the game — defined without jargon, with a link back to where you can see the idea in action.
27 terms
A straight, infinite line with a zero point and evenly spaced tick marks. Numbers to the right of zero are positive; numbers to the left are negative. The starting picture for every graph you'll ever draw.
See it on: the number line lesson.
A reference line used to measure position. The coordinate plane has two — a horizontal one (the x-axis) and a vertical one (the y-axis). Plural: axes (pronounced "ax-eez").
The horizontal axis. Positive x is to the right of the origin; negative x is to the left. It's the number line for the first coordinate of every point.
The vertical axis. Positive y is above the origin; negative y is below. It's the number line for the second coordinate of every point.
The point where the two axes cross — coordinates (0, 0). Every position on the plane is measured relative to it.
The number multiplied by a variable. In 3x + 5, the coefficient of x is 3. In −2x² + x, the coefficients are −2 and 1 (an invisible 1 in front of a lone x).
A flat surface with two perpendicular axes. Every point on it has a unique address of the form (x, y). Also called the Cartesian plane, after René Descartes, who introduced the idea in 1637.
See it on: the coordinate plane lesson.
Two numbers in parentheses, separated by a comma — like (3, −2). Order matters: (3, −2) and (−2, 3) are different points. The first number is the x-coordinate, the second is the y-coordinate.
One of the two numbers in an ordered pair. In (3, −2), 3 is the x-coordinate and −2 is the y-coordinate.
A formal name for the x-coordinate — the horizontal distance from the y-axis. You'll almost never hear this word outside of a textbook, but it's the "official" term.
A formal name for the y-coordinate — the vertical distance from the x-axis. Pairs with abscissa.
One of the four regions the axes divide the plane into. Numbered I–IV counter-clockwise starting from the top right:
(+, +)(−, +)(−, −)(+, −)An equation whose graph is a straight line. Every variable appears only to the first power — no squares, no cubes, no radicals. Standard shapes: y = mx + b or Ax + By = C.
See it on: lines & slope, the solver.
How steep a line is, and which way it tilts. Formally: rise over run — how much y changes when x increases by 1. A slope of 2 means "up 2 for every 1 right." A slope of −\u00bd means "down half for every 1 right." Usually written as m.
Where a graph crosses an axis. The y-intercept is where the graph hits the y-axis (found by setting x = 0). The x-intercept is where it hits the x-axis (found by setting y = 0). A line has one of each; a curve can have several.
A tidy way to write a linear equation: y = mx + b. The m is the slope; the b is the y-intercept. If you know those two numbers, you can draw the line without a calculator.
Two lines with the same slope and different y-intercepts. They point in the same direction and never touch.
Two lines that meet at a right angle. Their slopes are negative reciprocals of each other — flip one over and change the sign. Slopes 3 and −\u2153 are perpendicular; so are 2 and −\u00bd.
A rule that takes an input and produces exactly one output. Feed in an x, get back a y. Written as f(x) = …, read "f of x equals…". If a single input could give two different outputs, it's not a function.
See it on: the functions lesson, the calculator.
The set of all inputs a function is allowed to take. For most everyday functions the domain is all real numbers, but there are exceptions — you can't divide by zero, and you can't take the square root of a negative number (unless you leave the real numbers).
The set of all outputs a function actually produces. For f(x) = x², the range is "zero and up" — the parabola never dips below zero.
An equation or function of the form ax² + bx + c, where a ≠ 0. Its graph is a parabola — a U-shaped curve.
See it on: the solver's Quadratic tab.
The U-shaped curve that a quadratic function draws. Opens upward if a > 0, downward if a < 0. Every parabola has a single lowest (or highest) point called its vertex.
The turning point of a parabola — the lowest point if the parabola opens up, the highest if it opens down. For ax² + bx + c, its x-coordinate is −b / (2a).
The piece b² − 4ac hiding under the radical in the quadratic formula. It tells you how many real roots a quadratic has before you solve:
Two or more equations you want to satisfy all at once. Graphically, a solution to a system of two linear equations is a point where their lines cross.
See it on: the solver's System tab.
A value (or set of values) that makes an equation or inequality true. For 2x + 3 = 11, the only solution is x = 4. For x² = 9, there are two: x = 3 and x = −3.
When no value can make the equation or inequality true. Two parallel lines never meet, so a system built from them has no solution. Same for |x| = −3 — absolute value can't be negative.
When every value works. Happens when two equations describe the same line (the "system" is really one equation written twice), or when an inequality is true for all real numbers, like |x| ≥ 0.
A statement using <, >, ≤, or ≥ instead of =. Solutions are usually a whole range of values, not just one number. On a number line they show up as intervals or rays.
See it on: the solver.
A stretch of the number line between two endpoints. Written with brackets or parentheses — square brackets [a, b] include the endpoints; round parentheses (a, b) don't. On a graph, a filled dot means "included," an open dot means "not included."
The distance from a number to zero on the number line, written with bars: |x|. Distance is never negative, so |3| = 3 and |−3| = 3. When you see |expression|, read it as "how far this is from zero."
See it on: the solver's Absolute value tab.
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