Question

Can someone help me with this problem problem...

Answer 1

@HawkCrimson

Answer 2

Rearrange the first equation so it's in y = mx + b form. What is the difference between the two equations after you've rearranged?

@kevincourtes

Answer 3

@genius12 y=7x+8
y=-7x+7

Answer 4

You are close but not quite. You did one small thing wrong while rearranging.

Answer 5

1 would be the diferrence

Answer 6

@genius12 its -7x+8

Answer 7

It should be y = -7x + 8 and y = -7x + 7

You forgot the negative.

And yes you're write, the + 1 is the only difference here.

Answer 8

What does this difference of 1 mean?

Answer 9

What is the b in y = mx + b?

Answer 10

@genius12 i dont know, b is 1 right?

Answer 11

b is the y-intercept. The first line has a y-intercept of 8 and the other has a y-intercept at 7. That means that the graph with a y-int of 8 is shifted one unit up.

Answer 12

Now what do you notice about their slopes?

Answer 13

Are they the same/different?

Answer 14

@genius12 they're negative?

Answer 15

They are indeed negative, but are they the same or are they different?

Answer 16

@genius12 same?

Answer 17

@genius12 same?

Answer 18

Exactly! What do you know about lines with the same slope, (slope = rise/run) and different y intercepts

Answer 19

@genius12 they intercept each other?

Answer 20

Nope. Think about it, they have the same slope.

Answer 21

I'll give you a hint: same slope means parallel.

Answer 22

@genius12 so then they're parallel? sry i dont really know this

Answer 23

Ok. I'll draw a you a picture of what parallel lines are.
What do you notice about the two lines in the picture?

Answer 24

@genius12 they dont touch?

Answer 25

Exactly! Parallel lines are lines which always maintain the same slope and never cross each other.

Answer 26

So if y = -7x + 7 and y = y = -7x + 8 have the same slope, and DIFFERENT y-intercepts, then what does that mean?

Answer 27

@genius12 so they're dependant?

Answer 28

Nope.

Remember: Dependent means infinitely many solutions, i.e if I have two lines with the same equation, then they will lie on each other and so will have infinite solutions.

Independent means that the lines have just one solution.

Inconsistent means that there is no solutions.

Answer 29

If these two lines have the same slope, then they are parallel. They also have the different y-intercepts. So if they have different y-intercepts and are parallel (and parallel means they never cross each other), will the lines have a solution?

Answer 30

@genius12 i said dependant because the lines are infinite, but then i think its independant

Answer 31

Ok think about it. Two lines have the same slope. This means they're parallel since they are increasing/decreasing at the same rate, by rate I mean rise/run. So two lines are parallel and have different y-intercepts; this means that they will never cross each other at any point. Will they have a solution? Yes or no.

Answer 32

@genius12 ohhh ok, so no solution since they never touch

Answer 33

Exactly. So what would the system be? Dependent, independent, or inconsistent? (Look at the definitions I typed up)

Answer 34

@genius12 inconsisten

Answer 35

Exactly!

Answer 36

@genius12 thanks, can you help me with this last problem

Answer 37

And this can be supported graphically:Notice, because these lines have different y-intercepts and the same slope, they will be parallel and so will never have a solution! And this goes for any lines given in the form y = mx + b.

@kevincourtes

Answer 38

Open a new question for that.

@kevincourtes