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Feb 1 2018 06:32am
So I need to know how to best & easiest way transform equations from k form to general form and vice versa
so from y=kx+m to Ax+By+C=0 and vice versa

I think I'm doing it wrong initially

For example, I need to transform:
3x+y-1=0 & y-2x-6=0 to k form

I get it to y=3x+1 and y=2x+6, is this correct or did I mess up somewhere?
I'm very bad at maths but I'm trying to get better at it. Currently I'm having Mathematics 2B (that's what it's called in Sweden atleast)
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Feb 1 2018 07:52am
you are off with negative signs
imagine on 3x+y-1 = 0
your goal is to isolate it so that y is equal to something that resembles kx + m
in this case, k will be -3 (this is important) because you must subtract from both sides to get y alone
m becomes positive 1 because it must be added to each side to get y alone
so you are left with, in y=kx +m form, y=-3x+1, where as you can see k = -3 and m = 1

The second example is exactly the same but used different numbers.
again, just add or subtract to EACH SIDE whatever is needed to get y alone, as in the y = kx + m form.
The point is that you SHOULD NOT harm the equals sign. To meet this rule, you must always get y alone by adding or subtracting to BOTH sides (no change to the equals sign)
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Feb 1 2018 08:12am
Quote (ringo794 @ Feb 1 2018 03:52pm)
you are off with negative signs
imagine on 3x+y-1 = 0
your goal is to isolate it so that y is equal to something that resembles kx + m
in this case, k will be -3 (this is important) because you must subtract from both sides to get y alone
m becomes positive 1 because it must be added to each side to get y alone
so you are left with, in y=kx +m form, y=-3x+1, where as you can see k = -3 and m = 1

The second example is exactly the same but used different numbers.
again, just add or subtract to EACH SIDE whatever is needed to get y alone, as in the y = kx + m form.
The point is that you SHOULD NOT harm the equals sign. To meet this rule, you must always get y alone by adding or subtracting to BOTH sides (no change to the equals sign)


so where did I go wrong really? what is the correct y=kx+m on these 2 general forms?
don't really get it :(
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Feb 1 2018 08:16am
Quote (xaz @ Feb 1 2018 09:12am)
so where did I go wrong really? what is the correct y=kx+m on these 2 general forms?
don't really get it :(


you were correct in isolating y to the left, but since you went from 3x+y-1=0 to y = 3x-1, you have moved 3x and -1 to the other side but not changed their sign.
What really need to do to keep the equals sign true, is have the same change on each side. You have subtracted 3x from the left whereas you've added it on the right.
Clearly, these are not the same actions, so you equals sign is no longer true. if you subtract 3x from each side and subtract -1 from each side (add 1), you should end with my answer:
y = -3x + 1

This post was edited by ringo794 on Feb 1 2018 08:16am
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Feb 1 2018 08:19am
Quote (ringo794 @ Feb 1 2018 04:16pm)
you were correct in moving y to the left, but since you went from 3x+y-1=0 to y = 3x-1, you have moved 3x and -1 to the other side but not changed their sign.
What really need to do to keep the equals sign true, is have the same change on each side. You have subtracted 3x from the left whereas you've added it on the right.
Clearly, these are not the same actions, so you equals sign is no longer true. if you subtract 3x from each side and subtract -1 from each side (add 1), you should end with my answer:
y = -3x + 1


so it goes from
3x+y-1=0 to first:
moving the 3x to after equal sign making
y=-1=0+3x

then move the -1 to after equal sign with + sign to get rid of it in left side making
y=0+3x+1 correct?
then simplified to y=3x+1
so that's

k=3
m=1

correct or not? :) seems to make more sense now atleast
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Feb 1 2018 08:24am
Quote (xaz @ Feb 1 2018 09:19am)
so it goes from
3x+y-1=0 to first:
moving the 3x to after equal sign making
y=-1=0+3x

then move the -1 to after equal sign with + sign to get rid of it in left side making
y=0+3x+1 correct?
then simplified to y=3x+1
so that's

k=3
m=1

correct or not? :) seems to make more sense now atleast


sorry but nope
in your first paragraph you've added a 2nd equals sign. There should never be a second on in this sort of problem
You are simply adding or subtracting from each side in order to get y alone.
So think, if you have y +3x -1 = 0, what must you do to each side in order to get y on its own (as in the from we desire).
You clearly must subtract 3x, so do that on BOTH sides of the equals sign. Now you are left with
y - 1 = -3x.
Next to get y alone we must add 1 to BOTH sides
After this we are left with y = -3x +1 which is in k from where k = -3 and m = 1
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Feb 1 2018 08:30am
Quote (ringo794 @ Feb 1 2018 04:24pm)
sorry but nope
in your first paragraph you've added a 2nd equals sign. There should never be a second on in this sort of problem
You are simply adding or subtracting from each side in order to get y alone.
So think, if you have y +3x -1 = 0, what must you do to each side in order to get y on its own (as in the from we desire).
You clearly must subtract 3x, so do that on BOTH sides of the equals sign. Now you are left with
y - 1 = -3x.
Next to get y alone we must add 1 to BOTH sides
After this we are left with y = -3x +1 which is in k from where k = -3 and m = 1


ohh darn, don't know why I had 3x as positive and not -3x, ofc it has to become -3x because it's positive to begin with, if it was initially y-3x-1=0 then it would have been like I said right?
I'm sorry for the misunderstandings, this is really not my thing.. but theres always space for improvements I guess!

So I got y+3x-1=0

I then start by subtracting 3x on both sides leaving us with
y-1=-3x=0

Then we add 1 to both sides giving us y=-3x+1
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Feb 1 2018 08:32am
Quote (xaz @ Feb 1 2018 09:30am)
ohh darn, don't know why I had 3x as positive and not -3x, ofc it has to become -3x because it's positive to begin with, if it was initially y-3x-1=0 then it would have been like I said right?
I'm sorry for the misunderstandings, this is really not my thing.. but theres always space for improvements I guess!

So I got y+3x-1=0

I then start by subtracting 3x on both sides leaving us with
y-1=-3x=0

Then we add 1 to both sides giving us y=-3x+1


beautiful, you got it :p
the best way to get better is to keep making mistakes like these and understanding what went wrong and what to do next time :p
you'll get there of course if you keep trying
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Feb 1 2018 08:36am
Quote (ringo794 @ Feb 1 2018 04:32pm)
beautiful, you got it :p
the best way to get better is to keep making mistakes like these and understanding what went wrong and what to do next time :p
you'll get there of course if you keep trying


haha yay!! that makes me happy
i should mention that I need it in y=kx+m form so I can put it with the other one together in my calculator to form a graph and see where it edges with the other one

So lets see here.. inbefore I fail again
for the second calculation..

y-2x-6=0

Start by subtracting 2x
y-6=0+2x

now add 6 to both sides to get rid of 6 in left side

y=0+2x+6

y=2x+6 ???? :D

something seems fishy, can't be that easy :ph34r:
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Feb 2 2018 06:00pm
Quote (xaz @ Feb 1 2018 10:36am)
haha yay!! that makes me happy
i should mention that I need it in y=kx+m form so I can put it with the other one together in my calculator to form a graph and see where it edges with the other one

So lets see here.. inbefore I fail again
for the second calculation..

y-2x-6=0

Start by adding 2x
y-6=0+2x

now add 6 to both sides to get rid of 6 in left side

y=0+2x+6

y=2x+6 ???? :D

something seems fishy, can't be that easy :ph34r:


Fixed one small typo. You did the correct operation (addition) but stated the incorrect one (subtraction).

Yes, it is that easy when you get the hang of it! Nice work!
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