Linear System 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
Usually the horizontal axis in a Cartesian coordinate
system.
The measure of the steepness of a line that shows the line
slants downward from left to right.
x-axis
For example, y = -x + 2 has a slope of -1.
Decreasing Intervals
y-axis
Origin
x-intercept
The value of x when a given curve crosses the x-axis.
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.
Two lines that intersect at right angles.
Parallel Lines
Opposite Slopes.
Perpendicular
Usually the vertical axis in a Cartesian coordinate system.
Inequality
<  Solid line and shade below
Less Than
Greater Than
Less Than or equal to
>  Solid line and shade above
A relationship between two expressions that are not equal,
often written with the symbols >, >, <, and < that mean greater
than, greater than or equal, less than, less than or equal,
respectively.
<  Dotted line and shade below
>  Dotted line and shade above
Greater Than or equal to
System of Equations
Solution to a system
The solution to a system is the ordered pair when two or
more lines cross.
When given inequalities the solutions are anywhere in the
multiple shaded regions.
Substitution Method
The action of removing one unknown variable in an algebraic
equation either by the substitution of variables or by
cancellation.
A method of solving algebraic equations by replacing one variable with an
equivalent quantity in terms of other variable(s) so that the total number of
unknowns will be reduced by 1. For example, to solve the following
simultaneous equations:
x + y = 3 (1)
and
x - y = 1 (2)
we can first obtain x in terms of y using equation (1):
x = 3 - y (3)
Then, we substitute x with (3 - y) in equation (2):
Elimination
(3 - y) - y = 1 (4)
3 - 2y = 1
3 - 1 = 2y
2 = 2y
y=1
As shown, we reduce the number of variables in equation (2) from 2 to 1 using
the substitution method. As a result, we obtain a new equation with only one
variable. Therefore, we can solve for y. Next, we substitute y = 1 back to
equation (1) to solve for x:
x+1=3
x=2
A group of two or more equations that involve two or more variables.
When the number of variables is more than that of the equations, usually many
solutions exist. For example, x + y = 0. In this case, the number of solutions is
unlimited.
System by Graphing
When the number of variables is less than that of the equations, usually no
solution exists, because often there will be contradictory equations involved in
the given system.
For example, 2x = 0 and 5x = 1.
When the number of variables is equal to that of the equations, we have a better
chance of obtaining a unique solution to the system.
http://www.mathematicsdictionary.com/math-vocabulary.htm