Write the equation of the line which has a slope of 8/9 and passes through (7,-6). Write the answer in slope -intercept form. @e.mccormick

- YanaSidlinskiy

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- YanaSidlinskiy

I got some whacky answer such as:
y=8/9x-1
This is wrong and I need some help.

- e.mccormick

OK. so, y=mx+b
You have an (x,y) and are given an m. So you need to find b. You did that?

- YanaSidlinskiy

Well, my first step was in doing this: y-(-6) = 8/9(x+7)

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- YanaSidlinskiy

From there I went:
y+6= 8/9x+ umm...I did some weird thing like I subtracted 6 from the 7.. I hate fractions and I don't know how to solve it.

- e.mccormick

It is multiplication. The fraction times the fraction.
\(-6=\dfrac{8}{9}7+b\) is also \(-6=\dfrac{8}{9}\cdot\dfrac{7}{1}+b\)

- e.mccormick

Once you have that, you need to get all the # on one side and the b on the other... which means ether getting everything into ninths, or knowing how to work with mixed numbers.

- YanaSidlinskiy

Ok, I'll see what I can do. Can I just like multiply straight across?

- e.mccormick

For that 7/1, yes.

- e.mccormick

All numbers are fractions. The 1 just hides.

- YanaSidlinskiy

Yeah, I knew that. I got a mixed number: 6 2/9

- YanaSidlinskiy

Is there a way to like work without these fractions?

- e.mccormick

Not really, but fractions are your friend!

- YanaSidlinskiy

Yes, definitely....

- e.mccormick

OK, so, as a mixed number, what would you get if you then move those over to not be with the b?

- YanaSidlinskiy

Subtract?

- e.mccormick

Yes. You have to subtract it from both sides.

- YanaSidlinskiy

So wait. The equation that I have right now is:
-6= 8/9x + 6 2/9
Is that correct? I want to know before we actually move on...

- e.mccormick

No. You dealth with the 8/9x, you do not know the b.
-6 = 6 2/9 + b

- e.mccormick

See, you replaced the m, x, and y. You are finding b.

- e.mccormick

y = mx+b replace knowns to get:
(-6) = (8/9)(7)+b multiply out the 7 and 8/8 tp get:
-6 = 6 2/9+b
That is all the steps so far. Next is subtract 6 2/9 from both sides to get b alone.

- YanaSidlinskiy

Ok, lemme do it and see what I get...

- YanaSidlinskiy

Would this be the correct step before I do any of the subtractions?
-6 - (-6) 2/9

- e.mccormick

Not quite. Because it is postive on the one side, you subteact it or add the negative. That has one extra - sign...

- e.mccormick

-6 - (-6) = -6 +6 = 0, which is incorrect.

- YanaSidlinskiy

So wait, I'm so confused.

- YanaSidlinskiy

It would be -6 + -6?

- e.mccormick

Basically, yes.
-6 = 6 2/9+b
-6 - (6 2/9) = 6 2/9+b - (6 2/9)
Which also means:
-6 + (-6 2/9) = 6 2/9 - (6 2/9) +b

- e.mccormick

So what do you get when you simplify that?

- YanaSidlinskiy

Umm.... I don't know haha. This is terrible. I hate fractions!!!!

- YanaSidlinskiy

It's getting to the point where I'm about to blow up!!

- YanaSidlinskiy

-12? I'm guessing....

- e.mccormick

Well, it is a mixed number right now... so it just comes along for the ride. Because they are both negative, you are not going to need about converting both to fractions at the moment.
So yes, -12... and the fractin part. -12 2/9

- YanaSidlinskiy

So my slope-intercept would be:
y=1/8x -12 2/9?

- YanaSidlinskiy

THANK YOU JESUS I GOT THIS RIGHT!!!

- e.mccormick

Yah, that is it.

- YanaSidlinskiy

Thanks, Eric!! It really does look like I'm in love with fractions. Ughgh.

- e.mccormick

OK, I showed to this point:
\(-6=\dfrac{8}{9}\cdot\dfrac{7}{1}+b\)
Now, let me show you it all in factions from there.
\(-6=\dfrac{56}{9}+b\)
\(-6-\dfrac{56}{9}=\dfrac{56}{9}-\dfrac{56}{9}+b\)
\(-\dfrac{54}{9}-\dfrac{56}{9}=b\)
\(-\dfrac{110}{9}=b\)
So you can also write the slope-int as:
\(y=\dfrac{8}{9}x-\dfrac{110}{9}\)
Which graphs as:
https://www.desmos.com/calculator/4y3424y9ye

- YanaSidlinskiy

Oh!!! Ok. That's better!! Thanks!!

- YanaSidlinskiy

Not to offend you or anything like that, I was wondering why you started off with -6 = 8/9*7/1 +8...

- e.mccormick

I didn't. It is +b. Not +8.

- e.mccormick

Write the equation of the line which has a slope of 8/9 and passes through (7,-6).
That means:
(x,y) = (7,8) at one point, so x = 7 and y = -6 are valid in one equation.
m = 8/9
y=mx+b is the general equation. All I did was substitute what is known:
\((-6)=\left(\dfrac{8}{9}\right)(7)+b\)
That is how I started. It leaves only b as a variable, which is what I solved for next. =)

- YanaSidlinskiy

Ohhh!!!! Cuz I did it some other way and I got confused.....

- e.mccormick

Yah. Hehe. I can guess with a -1 in your first thing.
It is all about looking at what is known and unknown. They want it in y=mx+b form. They gave you 3 of the 4 variables, so you need to find the 4th.

- YanaSidlinskiy

Hehe. Not nice=) Just Kidding! But anyways.. I see where you're getting that "loved math" from.

- e.mccormick

People tend to shy away from fractions when they are first shoved on them, but they are really not that bad. I think they are just poorly taught. They come in handy, are in all of life, and prep you for dealing with a lot of other math.
For example, there are some similar rules for fractions and radicals:
To add or subtract, what is under must match.
To multiply, just go for it.
There are also some differences:
To divide a fraction, you flip over the divisor(second one) and multiply.
With radicals, they must be the same power to multiply or divide them. So square roots and cube roots won't multiply out the same way as two cube roots or two square roots.
So if you know how to work fractions it makes you partially ready for working with radicals (roots.)

- e.mccormick

And as for real life, a quarter is 1/4 of a dollar, a slice of pie is anywhere from 1/4 of a small one to 1/8th of a large one, yu can order half a sandwitch, the pitch (slope) of a roof in america is given in 12ths, etc.

- YanaSidlinskiy

Ohhh!!! Makes total sense. Went into depth with it! Thanks alot!!! I really appreciate it!!

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