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Hint:
|x| > k
breaks into
x < -k or x > k
where k is some positive number

is it still correct if the arrows go in the same direction when I graph it?

no the arrows should be going in opposite directions

oh so you flip the sign when you make k a negative?

exactly

what did you get

x> or equal to 12 and x < or equal to -18

good, you got it

thanks :D

you're welcome

use the slope formula
m = (y2 - y1)/(x2 - x1)

in this case
(x1,y1) = (-7,4)
(x2,y2) = (5,-3)

how do I find out whether the line rises, falls..etc ?

what did you get for the slope

-7/12

oh so the line decreases bc it has a negative slope?

you nailed it

sure I can help

all horizontal lines have a slope of 0

oh ok i understand

what if the x coordinates are equal? would that make the line vertical?

exactly

and the slope would be undefined

oh okay

how would i graph y=|x-3|?

do you know how to graph y = | x |

i think so? would there be 2 lines?

yes here is your blank xy axis
|dw:1359244103163:dw|

the graph of y = | x | looks like this
|dw:1359244135745:dw|

to graph y=|x-3|, you just shift over y = |x| three units to the right

im not sure i get you there...

but how do i know the coordinates to create the v shape

i understand the moving it to the right part

|dw:1359244469161:dw|

yes i understand that but what are the other coordinates for that shape?

for (3,0)..

(1,1) is on the original graph y = |x|
move that 3 units to the right to get (4,1)

|dw:1359244638800:dw|

(-1,1) is on the original graph y = |x|
move that 3 units to the right to get (2,1)

|dw:1359244675721:dw|

ohhhh so the slope for it is rise 1 over 1?

for the right half of it, yes

|dw:1359244723365:dw|

left half, slope is -1
|dw:1359244745927:dw|

ohhh ok so on the left side for any problem i will always decrease 1 and rise 1?

im trying to understand the concept so i can graph any absolute value problem

if it was |x| - 3, then you would move (0,0) to (0,-3)

but it's actually |x-3|

oh

would i be able to just plug this in to my calculator ?

yes you should be able to

do you know how to graph absolute value equations?

I guess I forgot :/

what kind of calculator do you have

i just found the absolute value button on my TI-83

and i put it into the y= and i got what you showed me earlier

ok great, glad you did

Solve the equation.
\[4x ^{2}-6x+9=0\]

you can either factor or use the quadratic formula

oh wait, one sec

no you can't factor, so you'll have to use the quadratic formula

how do you know you cant factor this problem?

oh okay, and i can use the discriminant as a test on any problem that looks like this one?

ohhhhh okay

solve the system of linear equations using any method.
2x+3y=47
7x-8y=-2
2x-y+3z=-19

solve the first two equations for x and y
once you have x and y, use them to find z

im not sure how i ended up with 111 for y... the answers say its wrong

no y should be 9, try it again

i did elimination with the first two equations

to get them to equal to 14 and -14 so they can cancel out but i keep getting 111

Oh! I understand now, thank you so much :)

you're welcome