Linear Equations Vocabulary Constant f(x) Coefficient The number part in front of the non-numerical symbol(s) in an algebraic expression, signifying multiplication. For example, the number 4 in the expression 4xy is a coefficient. An equation in which the highest power of any variable is one. Consecutive Numbers A symbol that stands for an unknown quantity. When we make a mathematics equation out of an ordinary statement by using a variable(s), it makes the thinking process mechanized and automatic, thus making the solution process much easier. Expressions The set of all possible values for the output of the function. Slope y-intercept The value(s) of a variable that satisfies a given algebraic equation. For example, x2 - 4 = 0 has two solutions: x = 2 and x = -2. The value of y when a given curve crosses the y-axis. Another name for gradient. Rise over Run Linear Equation y2 – y1 x2 – x1 The steepness of a line. Following on from each other in order. Variable For example, 1, 2, 3, and 4 are consecutive numbers. 5, 7, 9, and 11 are consecutive odd numbers. The measure of the steepness of a line that shows the slants upward from left to right. Solutions For example, y = x + 2 has a slope of 1. Increasing Intervals Coordinate Plane A plane formed by two intersecting and perpendicular number lines used to help locate the position of any point on a map or graph. Domain An algebraic expression is made up of three things: numbers, variables, and operation signs such as + and -. Following is a list of some examples: 2a a+b a2 ab Range The set of all possible input values for a function or relation. Function A quantity that does not change its value. In the equation y = 4x+1, the numbers 4 and 1 are constants. Function Notation The general form of a linear equation is y = mx + b, which is a straight line on a Cartesian coordinate graph. The parameter m is the slope of the line, and b is the y-intercept. Positive Slope A function of the type y = f(x) = ax + b because its graph is a straight line. Negative Slope A relationship between two variables that shows one variable decreases as the other one increases. x-axis A relationship between two variables that shows both variables increase or decrease together. y-axis Origin x-intercept The value of x when a given curve crosses the x-axis. A relation between two variables that vary together. If one variable always increases as the other increases, the relationship is said to be positive or direct. Otherwise, the relationship is negative or inverse. Data that is plotted as points on a graph to show a possible relationship between two sets of data. An arithmetic sequence is a sequence in which the difference between each term and the one after it is constant. For example, {1, 3, 5, 7, 9, ... }. This constant difference between successive terms is called the common difference. Arithmetic Sequence Each term after the first can be found by adding (or subtracting) the common difference. The general formula for the nth term in an arithmetic sequence is: an = a1 + (n-1)d in which an is the nth term, a1 is the first term, and d is the common difference. Geometric Sequence Parallel Lines Two or more straight coplanar lines that do not intersect. Same Slopes and different y – intercepts. The point where the reference axes in a coordinate system meet. The values of coordinates are normally defined as zero. Perpendicular Two lines that intersect at right angles. Opposite Slopes. A sequence in which each term (after the first one) bears a fixed ratio to its previous term. For example, 1, 2, 4, 8, 16... Scatter Plot Correlation Line of Best Fit Positive Correlation Negative Correlation The general formula for the nth term of a geometric sequence an is a1rn-1 in which a1 is the first term and r is the fixed ratio. Usually the vertical axis in a Cartesian coordinate system. Intuitively, a straight line drawn through as near as possible to the various points on a scatter diagram so as to best represent the trend. Usually the horizontal axis in a Cartesian coordinate system. Denoting the situation in which no apparent pattern can be formed when plotting data points for two variables in a scatter diagram. It shows that there is no relationship between the two variables. The measure of the steepness of a line that shows the line slants downward from left to right. No Correlation For example, y = -x + 2 has a slope of -1. Decreasing Intervals http://www.mathematicsdictionary.com/math-vocabulary.htm