###
4 way to describe Absolute Values graphs

stretch/shrink

vertical/horizontal/combo

vertex

opens up/down

###
slope intercept form

y=mx+b

###
slope formula for 2 points

y2-y1/x2-x1

###
two things needed for writing the equation of a line

point and slope

###
parallel lines have the _______ slope

same

###
Perpendicular lines have _________ slopes

opposite reciprocal

###
rational

Q

natural+whole+integers+all fractions and terminating decimals

###
real

R

natural+whole+integers+rational+irrational

###
natural

N

1,2,3,4,5,6,etc...

all positive whole numbers (not 0)

###
integers

Z

natural+whole+negative numbers

###
irrational

I

non terminating decimals without a pattern

###
commutative addition

A+7=7+A

operands can switch places

###
associative addition

a+(b+c)=(a+b)+c

###
distributive

a(b+c)=a**b+a**c

###
identity property of addition

a+0=a

###
commutative multiplication

A**7=7**A

###
associative multiplication

a**(b**c)=(a**b)**c

###
identity multiplication

a*1=a

###
inverse addition

a+(-a)=0

###
inverse multiplication

a*1/a=1

###
matrix

a rectangular structure used to organize data

###
identity matrix of addition for a 2x2

[0 0]

[0 0]

###
identity matrix of multiplication of multiplication for a 3x3

[1 0 0]

[0 1 0]

[0 0 1]

###
what must be true to add matrices together?

they must be the same size

###
how might you probe that 2 matrices are inverses of each other?

if you multiply them by each other and get an identity matrix and get multiplicative inverse matrices

###
what makes an absolute value equation shrink?

a fraction less than one before the abs. val. box

###
what makes an abs.val. box stretch?

a whole number greater than 1 before the box

###
dependent system

lines are equal, cross all same points

###
inconsistent system

it doesn't cross anywhere

###
independent system

crosses one point only

###
what is the difference between an equation and an inequality?

inequality has a variety of answers within a range, an equation can be inconsistent, independent, or dependent

###
horizontal translation

number inside the box

###
vertical translation

number outside the box

###
how to find the vertex of an abs. val. equation

opposite of number inside box (x), then outside number (y)

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