Question

would you know if this linear equation intersects or a parallel line? if it intersects, where does it intersects? 2x-y=2 and y=3x-4

Answer 1

There are two line rewritten
1) 2x-y=2
2) 3x-y=4

Answer 2

slopes are different so they intersect

Answer 3

One is not a factor of another so we know that they are not parellel

Answer 4

first one is
\[y=2x-2\] slope is 2 second line is
\[y=3x-4\] slope is 3

Answer 5

To find point of intersection set them equal to each other
2x-2=3x-4
and solve for x

Answer 6

so yes, they intersect. if you want to know where, set them equal and solve via
\[2x-2=3x-4\]
\[-2+4=3x-2x\]
\[-2=x\]

Answer 7

what imranmeah said

Answer 8

thank you...can i still ask ?

Answer 9

sure

Answer 10

why is that -2=x...? is it not 2=x?

Answer 11

Actually you are right; it is 2

Answer 12

can i ask still?

Answer 13

sure

Answer 14

you guys answered this so fast...mind teaching me what is the shortest method?..because i tried to answer ...it took me almost 3 hours but did not answer one...so, can u help ,e?

Answer 15

can you help me?

Answer 16

i still cant understand and i want to understand

Answer 17

If you are given two line and asked if they intersect,first thing you need to check is if they are parellel.

Answer 18

Because lines always intersect each other unless they are parellel

Answer 19

how to check if they are parallel or not?

Answer 20

Parellel lines have same slope, so following lines are parellel
y=3x+2
y=3x-5
y=3x+10
See same slope

Answer 21

yes clear...with that

Answer 22

with what I just said

Answer 23

but i was asked actually to solve those systems by graphing...

Answer 24

can u help me find the ordered pairs for me to graph?

Answer 25

please

Answer 26

Just graph two line and see where they cross

Answer 27

but i dont have given pairs...i need to know the pairs ,right?

Answer 28

what pairs?

Answer 29

of the x and y

Answer 30

example : 2x-y=2
y=3x-4

Answer 31

1)y=2x-2
2)y=3x-4


To graph 1) I would graph start at y intercept of -2 and move up with slope of 2

Answer 32

where do they intersect?....

Answer 33

ok i am following...and?

Answer 34

Do the same with second one.

After you have graph two line, see where they cross; that's the intersetion point

Answer 35

why move up with a slope of u? meaning, in the y axis?

Answer 36

i have a question....i have another example: x-2y=6 and y=x+1

Answer 37

in the book it will intersect at one point whose coordinates are -8 and -7...with the first line x-2y=6 it has a pair of 0 and -3 and 6 and 0....the next line y=x+1 it has pairs of -1 and 0 and 0 and 1....where did those pairs come from?

Answer 38

that is where i dont undestand

Answer 39

If you plug in 0 for x you should get -3 for y
x-2y=6
0-2y=6
y=-3

Answer 40

Plug in 6 for x-2y=6 in place of x and you get get y=0
6-2y=6
-2y=0
y=0

Answer 41

ya, but how did they get that? it is not given in the book

Answer 42

You choose a x value of your liking and figure out what y will be

Answer 43

oh..that is not a problem for me to solve?

Answer 44

nope

Answer 45

wow....how come the teacher did not say that?

Answer 46

one more? what about the slope?

Answer 47

what about it?

Answer 48

how would i know if the slope is positive or negative?

Answer 49

y=3x+2 positive slope
y=-3x+2 negative slope
you look that the number next to x

Answer 50

nex to x...that is 2?

Answer 51

Sorry "number with x"

Answer 52

ok...will look at first the samples and will ge tback to u if i am in trouble

Answer 53

by the way, where are u from? are u still going to school? u are such a smart boy...thank u