Question

graph the equation by plotting three points -3x+2y=2

Answer 1

can you change it to y = mx+b form ?
the first step is add+3x to both sides

Answer 2

0x+5y=5

Answer 3

no. just write +3x to both sides of
-3x+2y=2

Answer 4

-3x+3+2y+3=2+3

Answer 5

closer.... write +3x (not +3)

and when we add things to both sides, we do it only once per side (this is different from multiplying or dividing)

Answer 6

+3x-3x+2y=2+3x

Answer 7

yes. now notice on the left side 3x take away 3x is 0x or just 0
you get
2y= 2+3x
normally we write the "x term" first.... we are adding and 2+3x is the same as 3x+2 (order can be switched)

so
2y = 3x+2

now divide by 2 (when dividing, we have to divide *every* term)

Answer 8

2y/2=3x/2+2/2

1y=1.5x+1

Answer 9

yes. or just
y = 1.5x +1

in geometry, we normally keep the slope 1.5 as a fraction.
the slope 1.5 is the same as 1.5/1 change in y is 1.5 divided by change in x (1)
but we don't want 1.5 because you can't plot decimals.

so instead, write 1.5 as 3/2 so change in y (3 ) divided by change in x (2) are nice numbers.

we have
y = (3/2) x + 1

can you pick an x that gives a nice y ?

Answer 10

1

Answer 11

what is y when x is 1 ?

Answer 12

do i put 1 in the equation

Answer 13

yes...everywhere you see x, erase the x, and put in 1 instead

and remember (3/2)x is short for (3/2) times x

Answer 14

i got 2 1/2

Answer 15

yes, so (1, 2 1/2) or (1,2.5) or (1, 5/2) (all are the same thing)
but you don't like fractions or decimals. maybe a different x will give a nicer y ?

Answer 16

2

Answer 17

and x=2 means y = ?

Answer 18

4

Answer 19

so (2,4) is nice

now use the slope 3/2 = change in y divided by change in x
to find another point .

Answer 20

1.5,0.5

Answer 21

how did you get that ?

Answer 22

3/2 and 2/4

Answer 23

change in x means you add that to the x
change in y means you add that to the y

so if you are at
(2,4) and the slope is 3/2 you know the change in x is the bottom number (the 2) and the top number is the change in y (the 3)

Answer 24

so do i add 2+2 and 3+4

Answer 25

yes

Answer 26

4,7

Answer 27

now you need one more point.

you can also go backwards from (2,4)

if you go -2 in the x direction, you go -3 in the y direction
notice that (-3/-2 is the same slope as 3/2)

Answer 28

yeah

Answer 29

can you find a 3rd point ?

Answer 30

wait what two points do i have so far

Answer 31

2,4 and 4,7

Answer 32

2,4 and 3,2

Answer 33

ok

Answer 34

definitely NOT 3,2 (if you put x=3 in the equation you will not get y=2)

Answer 35

ok so to get my 3rd point do i do 2+4 and 3+7

Answer 36

yes, that will work

Answer 37

(2,4) (4,7) (6,10) are my three points?

Answer 38

if you plot them and draw a line through them you should get a nice line

Answer 39

ok thank you can you please help me with one more problem

Answer 40

notice the x values go 2,4,6 up by 2
and the y values go 4,7,10 up by 3
that means the slope is 3/2 (change in y divided by change in x is 3/2 )

notice if you go backwards: x down by 2, y down by 3 you get (0,1)

Answer 41

yeah

Answer 42

post the next one.