Algebra 1

variable

a letter or symbol that represents an unknown value of a number

expression

a problem with numbers, operations, and variables combined but no actual answer to the problems

equation

a statement that two expressions present are equal

constant

a number

formula

an equation that states a rule for a relationship among quantities

natural numbers

counting numbers

whole numbers

counting numbers including 0

integers

counting numbers including negative numbers (can’t be fractions or decimals)

Rational numbers

can be written as a fraction and includes decimals and negatives

irrational numbers

can’t be written as a fraction

r + r

r

r x r

r

r + i

i

r x i

i

i + i

i or r

i x i

i or r

Commutative Property

The order in which you add or multiply numbers does not change the sum or product of the numbers.

Associative Property

The way you group numbers when adding or multiplying does not change the sum or product of the numbers. (parentheses are important)

Identity Property

The identity of the number remains the same.

Inverse Property

You add or multiply the opposite to get the identity.

Multiplicative Property of Zero

The product of a number and 0 is 0.

Inequality

The relationship between two quantities that are NOT equal.

>

greater than,more than

<

less than, fewer than

>

more than or equal to, at least. no less than, a minimum of

<

less than or equal to, at most, no more than, a maximum of

compound

more than one; two or more parts

intersection

conjunction'; overlap

union

disjunction; gap

absolute value

distance from zero; always positive

Relation

A relationship between inputs and outputs

Function

A relation on where each input is related to exactly one output

Domain

Input, x-values, plug in, independent

Range

output, y-values, result, dependent

Discrete

No line or curve, distinct

Continuous

Infinite, has line or curve

X-intercept

when y equals 0; when the line passes through the x-axis

Y-intercept

when x equals 0; when the line passes through the y-axis

Slope

rate of change; rise divided by run

Positive slope

When the line goes up

Negative slope

when the line goes down

Horizontal slope

when slope equals zero

Vertical slope

when the slope is undefined

Slope-intercept form

y=mx+b

Point-slope form

y-y₁=m(x-x₁)

Parallel lines

lines that go on forever but never intersect

Perpendicular lines

2 lines that intersect to make a right angle

Standard form

Ax+By=C