medal
How do you write an equation to show the relationship between two
variables?

Question

medal
How do you write an equation to show the relationship between two 
variables?

legomyego180 · Answer

Any ideas?

kat_here2learn · Answer

not really can you ask me a question or give me somewhere to start? @legomyego180

kinged · Answer

You have to be given a relation first. Such that xRy (var. x is related to var. y).
For example, if x is five time larger than y, then x=5y.

kat_here2learn · Answer

im not really catching on

legomyego180 · Answer

So two variables, let pick two:
How about 2y and 3x.

To relate these variables we will set them equal to each other:
$$2y=3x$$
Now, it's important to get the y value on one side by itself so you can see what it looks like just by looking at the equation, if there is a 2 in front of it you wont be able to tell whats going on, its like trying to see the picture in a jigsaw puzzle, before you've put it together to what it is supposed to look like.

To get rid of the 2 we divide both sides by two:
$$\frac{ 2y }{ 2 }=\frac{ 3x }{ 2 }$$

The twos on the left side go away because 2 divided by 2 is one and we are left with:
$$y=\frac{ 3x }{ 2 }$$

or $$y=\frac{ 3 }{ 2 }x$$

Great, we have y all by itself on oneside, our "jigsaw puzzle" is put together, now we just need to remember a few math tricks from he last question you asked to help us figure out what this line would look like.

So remember, the number in front of the "x" is your slope, here it would be $$\frac{ 3 }{ 2 }$$

To figure out the y intercept (where the line crosses the y axis) we set X (dont get mixed up here!) equal to zero:

$$y=\frac{ 3 }{ 2 }x \rightarrow y=\frac{ 3 }{ 2 }\times0\rightarrow y=0$$

So our y intercept is zero.

to find our x-intercept we set y equal to zero then solve for x

$$0=\frac{ 3 }{ 2 }x$$

In this case x would equal 0 because the only thing you can multiply 3/2 by to get zero is zero.

Does that help?

kat_here2learn · Answer

so the relationship between two values is that y=x+1?

legomyego180 · Answer

technically, the relationship is:

$$y=mx+b$$

where m is the slope and b is the y intercept

kat_here2learn · Answer

quick questionWhen is it helpful to convert from point-slope to slope-intercept form?

phi · Answer

it's easier to plot if in slope-intercept form

kat_here2learn · Answer

so when your plotting?

legomyego180 · Answer

yep

kat_here2learn · Answer

just to make sure my answer for the first question is y=mx+b?

kat_here2learn · Answer

@legomyego180