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direct variation

y=kx

inverse variation

y=k/x

4 way to describe Absolute Values graphs

stretch/shrink

vertical/horizontal/combo

vertex

opens up/down

vertical/horizontal/combo

vertex

opens up/down

standard form

Ax+By=C

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

slope of y=3

0

slope of x=-7

undefined

rational

Q

natural+whole+integers+all fractions and terminating decimals

natural+whole+integers+all fractions and terminating decimals

real

R

natural+whole+integers+rational+irrational

natural+whole+integers+rational+irrational

natural

N

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

all positive whole numbers (not 0)

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

all positive whole numbers (not 0)

whole

W

natural+0

natural+0

integers

Z

natural+whole+negative numbers

natural+whole+negative numbers

irrational

I

non terminating decimals without a pattern

non terminating decimals without a pattern

commutative addition

A+7=7+A

operands can switch places

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

zero property

a*0=0

matrix

a rectangular structure used to organize data

identity matrix of addition for a 2x2

[0 0]

[0 0]

[0 0]

identity matrix of multiplication of multiplication for a 3x3

[1 0 0]

[0 1 0]

[0 0 1]

[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)