im trying to find the slope of a line with equation 2x+3y=6

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- anonymous

im trying to find the slope of a line with equation 2x+3y=6

- chestercat

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- anonymous

You need the form y = mx+b. So manipulate the equation to isolate Y.

- anonymous

and m would then be my answer>

- anonymous

Yes, you are looking for m.

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- anonymous

practically , - x's coefficient / y's coefficient so , -2/3

- anonymous

So I would first subtract the 2x to the other side, leaving 3y = -2x +6.

- anonymous

Then you divide by 3 since 3y/3 would just leave you with y.

- anonymous

divide both sides by 3 that is.

- anonymous

ok. so if someone asks write the equation of the line through(2 -3) and parallel to y= 4x -1 how would i do thta

- anonymous

Ok you know that the point (2,-3) is going to be on the line of your answer. If two lines are parallel, that means they have the same slope.

- anonymous

So you would substitute your points in, giving you -3 = 4*2 + b

- anonymous

So you have -3 = 8+b. What value of b do you need to make -3 = 8?

- anonymous

11

- anonymous

Be careful. You need -11.

- anonymous

So since -11 is your b value, you construct your equation. y = 4x - 11. You know that it's 4x because if two lines are parallel they have the same slope. We did those calculations to determine your b value.

- anonymous

so it goes back to the original y- 4x-1?

- anonymous

No. Your answer would be y = 4x -11. This line is parallel to y = 4x -1 because they share the same slope.

- anonymous

the -3= 8 +b is used to find the parallel slope that i need

- anonymous

No, the -3 = 8 +b is used to determine your b value (Your y-intercept)

- anonymous

Two lines are parallel if they share the same slope. that's why you already know your slope for the problem because your answer has to have the same slope as your original line.

- anonymous

can we do one more with different points?

- anonymous

Sure. Do you have an example?

- anonymous

(2 -5) parallel to y=2x+3

- anonymous

Ok. Looking at y = 2x +3, What is the slope of our ansewr going to be?

- anonymous

since they must be parallel

- anonymous

should be 2?

- anonymous

Correct. So for our answer equation right now we have y = 2x + b. Now we must find out b value, and since we are given a point (2,-5), we plug those points into our equation to find our b.

- anonymous

ok so its -5= 2x+b

- anonymous

You forgot to plug in your value for x.

- anonymous

-5 = 2*2 +b

- anonymous

ok. -5=4 +b

- anonymous

Correct. Now what b value do we need to make that equation true?

- anonymous

-9

- anonymous

Correct. Now what's our answer?

- anonymous

this is where i get confused... how do i find this answer

- anonymous

Oh ok. Well the question asks for a line, so we know our answer will be an equation of a line. We need the general form of our answer (meaning leaving x and y as x and y in the answer). We calculated our b value and we know our m value since it has to be parallel to our starting line. y = mx + b. Fill out that equation with the information we calculated (m value and b value).

- anonymous

well slopes the same and b is -9 so its y=2x-9?

- anonymous

Absolutely correct

- anonymous

so on this everything fallls back to y=mx+b?

- anonymous

Now if you get an answer and your not sure about it, you can just plug in your given point into your answer and if you get the same thing on both sides the equation of your line works with your point.

- anonymous

In this question yes it does. Since your looking for a line your answer will be in the form of y=mx+b

- anonymous

and what if it asks for perpendicular? (1,-1) perpindicular to y=2x+4

- anonymous

Ok a Perpendicular line will have a slope that is the negative reciprocal of the slope of another line. So in this example look at 2 as (2/1). A reciprocal is when you flip the denominator and the numerator, so my reciprocal of 2/1 would be 1/2. Put a negative sign on that and that's the slope of my perpendicular line.

- amistre64

Pops is suited up eh..... that a missionary photo :)

- anonymous

We will calculate our b value the same way as we did before.

- anonymous

Yeah yeah I hear ya lol

- anonymous

ok so -1=2(1) +4

- anonymous

No you plug in your new slope to find the b value. Your new slope would be -1/2

- anonymous

So we would have -1 = -(1/2)*1 + b

- anonymous

so on these you automatically flip the slope

- anonymous

On a perpendicular line yes. And you change the sign.

- anonymous

ok so -1/2 *1 plus b

- anonymous

Right.

- anonymous

so then b would be 1/2?

- anonymous

It would be -1/2. You have -1 = -(1/2)*1 + b. -1/2 times 1 is just -1/2. So we're left with -1 = -1/2 + b. b has to be -1/2

- anonymous

two negatives make a positive. so then we plug this back in to y=-1/2x+-1/2?

- anonymous

Two negatives make a positive in multiplication, not addition.

- anonymous

But yes your equation is correct.

- anonymous

And that's your answer.

- anonymous

awesome man i think i got it im having to teach myself this stuff cause i missed days lol

- anonymous

Yeah. If you have a graphing calculator you can understand it better if your a visual learner. I'm more of a hands on / visual type learner myself so it helped me years ago when I was learning this stuff

- anonymous

yea. the only way i learn is to beat it into my head lol. well thanks man can i add you on this site somehow in case i get in a rut?

- anonymous

well you can add me as fan. Idk if it will do anything but I try to get on here some.

- anonymous

ok thanks man

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