Question

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

Answer 1

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

Answer 2

and m would then be my answer>

Answer 3

Yes, you are looking for m.

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

divide both sides by 3 that is.

Answer 8

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

Answer 9

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.

Answer 10

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

Answer 11

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

Answer 12

11

Answer 13

Be careful. You need -11.

Answer 14

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.

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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.

Answer 20

can we do one more with different points?

Answer 21

Sure. Do you have an example?

Answer 22

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

Answer 23

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

Answer 24

since they must be parallel

Answer 25

should be 2?

Answer 26

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.

Answer 27

ok so its -5= 2x+b

Answer 28

You forgot to plug in your value for x.

Answer 29

-5 = 2*2 +b

Answer 30

ok. -5=4 +b

Answer 31

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

Answer 32

-9

Answer 33

Correct. Now what's our answer?

Answer 34

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

Answer 35

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).

Answer 36

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

Answer 37

Absolutely correct

Answer 38

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

Answer 39

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.

Answer 40

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

Answer 41

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

Answer 42

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.

Answer 43

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

Answer 44

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

Answer 45

Yeah yeah I hear ya lol

Answer 46

ok so -1=2(1) +4

Answer 47

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

Answer 48

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

Answer 49

so on these you automatically flip the slope

Answer 50

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

Answer 51

ok so -1/2 *1 plus b

Answer 52

Right.

Answer 53

so then b would be 1/2?

Answer 54

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

Answer 55

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

Answer 56

Two negatives make a positive in multiplication, not addition.

Answer 57

But yes your equation is correct.

Answer 58

And that's your answer.

Answer 59

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

Answer 60

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

Answer 61

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?

Answer 62

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

Answer 63

ok thanks man