Question

Two lines are represented by the equation x+2y=4 and 4y-2x=12. Determine weather the two lines are parellel, perpendicular or nither. Justifiy your answer.

Second Question:
Find the image of the point (-1,4) after the transformation T 3,-5 followed by r y axis.
Please HELP AND SHOW ALL WORK!!!!

Answer 1

write both lines in slope intercept form

2y = -x + 4 or y = -1/2 x + 2 (line 1)

4y = 2x + 12 or y = 1/2 x + 6 (line 2)

what are the slopes of Line 1 and Line 2?

Answer 2

you need to solve each equation for y to find the slopes

x+2y=4

2y = -x + 4

y = -x/2 + 4/2

y = -1/2x + 2


So the slope of the first line is -1/2

4y-2x=12

4y = 2x + 12

y = 2/4x + 12/4

y = 1/2x + 3

So the slope of the second line is 1/2


Are these slopes equal?

Answer 3

Rule:

If two lines have equal slopes, then they are parallel lines

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Rule:

if two lines have slopes of m and n, then they are perpendicular if

m*n = -1

Answer 4

so these two lines are ______

Answer 5

they are equal?

Answer 6

1/2 is equal to -1/2???

Answer 7

no so there not =?

Answer 8

so they are NOT parallel lines

Answer 9

what about perpendicular?

Answer 10

so they would be perpemdicular

Answer 11

why is that

Answer 12

because the slopes atre different and ones positive and the others negative

Answer 13

the two slopes have to multiply to -1

Answer 14

do the two slopes 1/2 and -1/2 multiply to -1 ?

Answer 15

uhm.... no

Answer 16

i got -0.25

Answer 17

they multiply to -1/4 or -0.25, which is NOT -1

Answer 18

good

Answer 19

so they are NOT perpendicular either

Answer 20

so they are neither?

Answer 21

yep

Answer 22

they intersect, but they don't intersect at 90 degree angles

Answer 23

okay thanks how about the second prob?

Answer 24

T 3,-5 sounds like

(x,y) ----> (x+3, y-5)

Answer 25

(x,y) ----> (x+3, y-5)

(-1,4) ----> (-1+3, 4-5)

(-1,4) ----> ( ??, ?? )

Answer 26

-1?

Answer 27

4-5 = -1 good

Answer 28

-1+3 = ??

Answer 29

2?

Answer 30

(x,y) ----> (x+3, y-5)

(-1,4) ----> (-1+3, 4-5)

(-1,4) ----> ( 2, -1)

Answer 31

that's after we do the translation rule (x,y) ----> (x+3, y-5)

Answer 32

now you reflect it over the y axis, so you just change the sign of the x coordinate to go from +2 to -2

Answer 33

so the answer is (2,-1)?

Answer 34

no you have to reflect over the y axis

Answer 35

so it would be both -2 and -1?

Answer 36

(-2,-1) yes

Answer 37

how do I show the work on my psper?

Answer 38

you first show how you go from (-1,4) to ( 2, -1)

Answer 39

by using the translation rule (x,y) ----> (x+3, y-5)

Answer 40

so i write that ^

Answer 41

yeah and show how to go from (-1,4) to ( 2, -1)

Answer 42

using what I wrote above

Answer 43

then you have to reflect (2,-1) over the y axis to get (-2, -1)

Answer 44

okay thanks... Can I have help with another?

Answer 45

sure, one more

Answer 46

i posted it

Answer 47

ok