GLOSSARY

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To ADD integers with different signs, SUBTRACT the lesser absolute value from the greater absolute value.  Give the result the same sign as the integer with the greater absolute value.

For all numbers a, b, and c, the following are true:

1.  If a > b, then a + c > b + c
                    and a - c > b - c

2.  If a < b, then a + c < b + c
                    and a - c < b - c

In words, if the same number or expression is added or subtracted from both sides of a true inequality, the new inequality is also true.
see lesson

For any number a,

a + 0 = 0 + a  

In words, adding zero to a number leaves the number unchanged, hence the "identical" number.

For every number a, a + (-a) = 0

e.g.

5 + ? = 0     5 + (-5) = 0

-17 + ? = 0    -17 + 17 = 0

In words, if the opposite of a number is added to the original number, the sum is equal to zero.

A line drawn so it is close to most or all of the data points in a graph.

A best-fit line is described as strong or weak depending on how close the data points are on average.
see lesson

Coordinate Plane  

The difference of squares can easily be factored as follows:

a² - b² = (a + b)(a - b)
x² - 49 = (x + 7)(x - 7)

See Multiplication Property for Inequality

In the monomial term 3bc, there are three factors: 3, b and c.

In the algebraic expression 3(m+5) there are two factors: 3 and (m+5). 

F  the first terms,
O  the outside terms,
I    the inside terms, and... 
L   the last terms

(see vertical line test)

For all numbers a, b, and c, the following are true:

IF c is POSITIVE:

1.  If a > b, then ac > bc
2.  If a < b, then ac < bc

the same holds true for DIVISION where c is not equal to zero.

+ + + + + + + + + + + + 

For all numbers a, b, and c, the following are true:

IF c is NEGATIVE:

1.  If a > b, then ac < bc
2.  If a < b, then ac > bc

the same holds true for DIVISION where c is not equal to zero.

a ^. 1 = 1 ^. a = a

In words, a number multiplied by its reciprocal will always equal zero.

a ^. 0 = 0 ^. a = 0  

In words, any number or expression multiplied by zero will equal zero.

For a given point (x₁, y₁) on a non-vertical line having slope m, the point-slope form is: 

y - y₁ = m(x - x₁)  

see lesson

For any numbers a and b and any integers m, n, and p:

(a^mbⁿ)^p = a^mpa^np

(a^m)ⁿ = a^mn

For any numbers a and b and any integers m:

(ab)^m = a^mb^m

a^maⁿ = a^m+n

a^m/aⁿ = a^m-n

The relationship ^a/_b of two quantities a and b that are measured in different units.  For example, a car that travels 100 miles in 2 hours has a unit RATE of speed of 50 miles per hour, or  ^{50 miles}/_{1 hour}

a = a

Given the slope m and the
y-intercept b of a line, the equation of the line is:

y = mx + b  

The Standard Form of a linear equation is:

Ax + By = C

where A, B, and C are integers, A > 0 and A and B are both not equal to 0.
see lesson

To subtract a number, add its additive inverse. For any numbers a and b;

a - b = a + (-b) 

See Addition Property for Inequality

if a = b, then b = a

With respect to a system of two linear equations, we can say the system has either:
a) one solution (intersecting lines)
b) infinite solutions (same line)
c) no solution (parallel lines).

if a = b and b = c, then a = c

a⁰ = 1