Question

Help with one slope points problem?



Find the equation of the line below. Arrange your answer in the form y = mx + b, where b is the constant.


Points (-2,2) and (2,-2) and my answer is y = x.. it doesn't seem right.

Answer 1

i dont think its right there

Answer 2

do you know the formula for finding the slope of a line given 2 points...?

Answer 3

Find the slope of the line...

Answer 4

Yes. I do know the formula...

Answer 5

The slope is 4, right?

Answer 6

Then substitute the values in the formula and find the slope first...

Answer 7

No it is not right...

Answer 8

well looking at your solution, the gradient is correct...

so the line is

y = x + b

to find the value of b, just substitute the x and y values from either point and solve for b

Answer 9

Can you show your work so that we can find where you went wrong ??

Answer 10

oops the slope is -1 not 1

so the line is

y = -x + b

Answer 11

Okay.. 2 = -2 + b?

Answer 12

What next?

Answer 13

What are you doing ???

Answer 14

Have you find the slope ???

Answer 15

*found.

Answer 16

No..

Answer 17

What is slope according to the formula you know ??

Answer 18

\[Slope = \frac{y_2 - y_1}{x_2 - x_1}\]

Answer 19

That's where I'm stuck... I thought it was 4 down and 4 across, wait, is the slope 0?

Answer 20

No it's not..

Answer 21

Just substitute the values in the above slope formula and be careful with negative signs..

Answer 22

So I have -4 and positive 4....

Answer 23

slope = 8?

Answer 24

Yes..

What you get on dividing them ??

Answer 25

um. what do I divide them by?

Answer 26

\[y = \frac{-2 - (2)}{2 - (-2)} \implies \frac{-4}{4} \implies ??\]

Answer 27

-1

Answer 28

Then what is the problem you are facing in finding the slope.

This is the standard procedure for finding the slope..

Getting??

Answer 29

Understood.

Answer 30

Just remember the formula It will help you in lot of problem like we are doing..

Answer 31

Now:

y = mx + b

Or by putting m = -1 (m is notation for Slope)

y = -x + b

Is it okay ??

Answer 32

ok, y = -1x + b

or y = -x + b

Answer 33

Yep..

Now :

Substitute any of two point given in it to find b...

Answer 34

so I can use -2 and 2?

Answer 35

Your first point is (-2,2)..

Here x = -2 and y = 2..

Answer 36

If you don't want to use the first point then use the second simple..!!

(2, -2)

here x = 2 and y = -2..

It is your wish to choose any one you want...

Answer 37

Now substitute any one point and find b...

You will get b same for both the cases...

Answer 38

so if 2 = -2 + b.. is b a 4?

Answer 39

If you are not getting then tell me, I will follow another method to make your understand this..

Answer 40

I honestly don't understand.

Answer 41

What is the step you are not getting ??

Answer 42

Have you got how we found slope ??

Answer 43

I understand how to find the slope, but this confused me:

Now substitute any one point and find b...

You will get b same for both the cases...

Answer 44

Ha ha ha ha..
Okay..

I just said if you put first point or if you put second point, you will get the same value for b in both the cases..

Answer 45

Okay, that helps a bit.. so what points do I use, and after that, how do I find the value for b?

Answer 46

Just forget what I just said..
Tell me what is first point given to you ??

Answer 47

Um, let's see.. .(-2,2)

Answer 48

Yep..

Now tell me what is x and what is y here ??

Answer 49

x is -2, y is 2.

Answer 50

Now you have ater putting slope :

y = -x + b

Right ??

Can you substitute here x and y values to find b ??

Answer 51

*after

Answer 52

2 = -2 + b

Answer 53

ok, then..

Answer 54

Yep..

Now 2 both the sides and find b here..

Answer 55

b = 4

Answer 56

Yep..

Now you have again :

y = mx + b

Right ??

Answer 57

Yes..

Answer 58

Here, you have found m = -1 and b = 4 (b you have just found)..

Here put these values in the equation : y = mx + b

and tell me what do you get ??

Don't put values of x and y here.. Just leave them as x and y..
Tell me what did you get??

Answer 59

y = -1x + b

Answer 60

or y = -x + b

Answer 61

Substitute for b also..

Answer 62

y = -x + 4

Answer 63

You have found the value of b just above you can safely put it here..

Yep..

So:

y = -x + 4 is your required equation..

Answer 64

well, thanks so much for your help.

Answer 65

Welcome dear..