The new forums will be named Coin Return (based on the most recent vote)! You can check on the status and timeline of the transition to the new forums here.
The Guiding Principles and New Rules document is now in effect.
Slope of a line
Fizban140
Registered User, __BANNED USERS regular
Registered User, __BANNED USERS regular
For whatever reason my math book will not explain this, how do I find a line when I know the slope and the first set of coordinates? This seems really simple but my book never explains how to translate a slope.
This book is worthless it really does not explain anything beyond an incredibly simple example and then the homework goes far, far beyond that.
I have to find the slope of line 1. Line 1 contains point 3,4 and is perpendicular to -5,1 and 3,-2 I got 8/1 but that is wrong it is suppose to be 8/3
This book is worthless it really does not explain anything beyond an incredibly simple example and then the homework goes far, far beyond that.
I have to find the slope of line 1. Line 1 contains point 3,4 and is perpendicular to -5,1 and 3,-2 I got 8/1 but that is wrong it is suppose to be 8/3
Fizban140 on
0
Posts
Let's take a line with slope 1/4, with point (0, 4) on that line. In this case, to find the next point in the line, you'd start at (0, 4) and move one point up, then four points to the right. You would be at point (1, 8), which is now confirmed to be on the same line.
If you need a third point, simply start over at your given point and go backwards- one point down, then four points to the left. In this example, you're now at point (-1, 0)- which is on the same line.
EDIT: Key word in that problem is perpendicular. To find a perpendicular line, you take the slope of the first line and change it. For example:
1) A line with slope 3 has a perpendicular line with slope -1/3.
2) A line with slope -3 has a perpendicular of 1/3.
3) A line with slope -1/3 has a perpendicular of slope 3.
4) A line with slope 1/3 has a perpendicular with slope -3.
I can has cheezburger, yes?
so perpendicular means the slope is the negative inverse(/opposite) of the slope of the line it is perpendicular to
so since slope is rise (difference in y coordinates) over run (difference in x coordinates),
the slope of the line it is perpendicular to is (1 - (-2))/(-5-3) = -3/8
and the negative inverse of that is 8/3
questions?
m=(y[2] - y[1])/(x[2]-x[1])
I hate typing math without the use of subscripts and stuff, but the number in the brackets [] are subscritpted.
basically you slope is equal to y2 - y1 divided by x2 - x1.
I can has cheezburger, yes?
I have 3,5 and the slope is -2/3.
This massively confusing equations says I should do y-5 = -2/3 (x-3)
I do not know why I should do that or how it works but that is what the book wants, I think.
I ended up with y = -2x + 24/3 this seems so wrong.
y= -2/3x +8 now how do I make this a line? x=-12? I think I messed up. -12,0 maybe?
m = slope of the line
b = y-intercept of the line (where the line crosses the y-axis)
You want, first, to get your equation right. It gives you m- the slope- now all you need to do is walk it back until it crosses the y-axis. You're given -2/3 for slope and (3, 5) for a point on the slope. Let's walk it backwards.
Two points up (remember, negatives move the other direction when finding points on a slope) takes us to (3, 7). Three points left takes us to... (0, 7). Congrats- there's your y-intercept and you can solve the problem.
The answer is: y = (-2/3)x + 7.
I can has cheezburger, yes?
h -> y-coordinate of the point you were given.
k -> x-coordinate of the point you were given
m -> slope
Just memorize that, 'cause you'll use it a lot.
So for example, if you need to write the equation of the line through (-4, 1) with a slope of 2, it would be:
y - -4 = 2(x - 1) or
y + 4 = 2(x - 1)
What you were trying to do was put it into slope-intercept form, which is the way everyone teaches for some reason. (slope-intercept for is y = mx + b, where m is the slope again and b is the y-intercept, the point where the line hits the y axis.)
3DS Friend Code: 3110-5393-4113
Steam profile
I wish my book explained it like forum posts, it is so much easier this way.
I can has cheezburger, yes?
This drove me nuts when I was tutoring in college, as an aside.
Please learn what kime said to begin with, it is the best one to learn. Especially for Calculus.
Example? I want to say yes, but I'm afraid if I'm misinterpreting your question I'll be giving the wrong answer.
Oh yeah, that works too. Whichever method he likes the best, really. I like point-slope form better, especially in situations like that where it's just a plug-it-in question, but either way works.
3DS Friend Code: 3110-5393-4113
Steam profile
The easiest way that I see doing it is getting rid of the fraction, so multiply everything by 8, right?
y + 12 = -2/8(-1 - x)
y + 12 = -1/4(-1 - x)
y + 12 = 1/4 + 1/4x
Unless you're solving for y it would be easier to multiply the y + 12 by 4 instead of dividing the (-1 - x), though.
I'm assuming that the (-1 - x) isn't in the denominator, and that you actually have -2/8 in front of (-1 -x). It's hard to tell, but this makes more sense based on your question about the fraction.
In the example you gave, the thing in the parentheses is being multiplied by 2/8. So to get rid of the fraction, you multiply everything by 8. However, "everything" is a little weird in these situations. What you do is treat everything separated by a + or a - as one thing. But if they are not separated by a + or -, if they are just being multiplied or whatnot, then everything being multiplied is one thing.
So 1 + 2 - 3 = 0 has 4 parts. The 1, 2, and 3 are separated by a + or a -, doesn't matter which. And then the 0 is all by itself.
But 1(2) - 3 = -1 only has three distinct parts. The 1 and 2 are being multiplied, are not separated by a + or -, so are treated as one thing for the sake of what we are doing here.
So in your situation, you have: y + 12 = -2/8(-1 - x).
You have y.
You have 12.
And you have -2/8(-1 - x). The part in the parentheses is separated by those parentheses for a reason, the -1 - x is grouped together. So really, you've got the -2/8 and the (-1 - x) being multiplied. And as above, when there's no + or -, it's one part.
So to get rid of the fraction, you would multiply everything by 8.
Multiply y by 8 to get 8y.
Multiply 12 by 8 to get 96.
Multiply -2/8(-1 - x) to get -2(-1 - x).
The last one is the trickiest. Should I go over that in more detail? Or am I already rambling and not making sense :P?
Also, what was the problem initially? "Get rid of the fraction"? "Solve for y"? "Graph"?
And I'm fully aware that since it took me so long to write this horrible explanation I'm probably way to late. But phooey to all the people who possibly beat me. I'm better!
Edit: Yeah Jayson, talking to you! And wow this is really long and probably not helpful. I should definitely refrain from giving math advise this late. Erm, this early. Whatever.
3DS Friend Code: 3110-5393-4113
Steam profile
Also if I am diving something like this 2-3x/3 do the 3s cancel out and I am left with 2? That is how the teacher in class did it and I am not sure why that works. If I do 2-3 I would have -1/3 which is different, I know there is an x but it should work without the x right? Or am I left with 2-x?
My book never really explained it but I have -8,-2 with a slope of -3/5 how do I turn this into standard form? I also have to find the equation of the line.
It's difficult to tell if you're talking about (2-3x)/3 where 2-3x is all on top of the fraction, or 2 - (3x/3) where just the 3x is on top and the 2 is by itself. But unless x=0 you shouldn't be left with just 2 either way.
Case 1: (2 - 3x)/3
You can divide each component (2 and -3x) separately by 3, to get (2/3) - ((3x)/3). All these parentheses are ugly, but without writing it out and scanning it I don't have a more elegant method. 2/3 is by itself, and (3x)/3 can be reduced -- that is, you can divide both the top and bottom of the fraction by 3 -- to get x/1, which is the same as just x. So the end result is (2/3) - x.
Case 2: 2-(3x/3)
You just skip to the reducing step, so divide both the top and bottom of 3x/3 by 3 to get x. End result: 2 - x.
I'm not sure how standard form is different from the equation of the line. But the point-slope form mentioned earlier is what you want to start with when you have a point and the slope.
y - y1 = m(x - x1)
Where x1,y1 are the coordinates of your point, and m is the slope. Plug in your values to get
y - (-2) = (-3/5)(x - (-8))
From there, you can multiply out the slope and move the constant on the y side (that is, 2) over to the x side.
y + 2 = (-3/5)(x + 8)
y + 2 = (-3/5)x + ((-3/5)8)
y + 2 = (-3/5)x - (24/5)
y = (-3/5)x - (24/5 - 2)
y = (-3/5)x - (24/5 - 10/5)
y = (-3/5)x - (34/5)
==
Alternatively, you can start from
y - (-2) = (-3/5)(x - (-8))
and instead of solving for y, you can plug in x=0 to find out the y-intercept.
y - (-2) = (-3/5)(0 - (-8))
y + 2 = (-3/5)(8)
y + 2 = (-24/5)
y = (-24/5) - 2
y = (-24/5) - 10/5
y = -34/5
You already know the slope is -3/5.
The standard form of the equation for a line is y = mx + b, where m is the slope and b is the y-intercept (-34/5).
y = (-3/5)x + (-34/5)
y = (-3/5)x - (34/5)
=====
I feel that it might be worth going into a more explanation of fractions, line graphs or the algebraic method of solving equations, since it seems like at least one of these isn't being completely understood, but I'm not sure which one. This isn't just a leg-pulling like that fake girl thread a few months back, is it?
If you know what you're doing now I don't want to bring in more and mess things up, but I did just want to note something. If your book is asking for "Standard Form" as you mentioned above, that's a specific way of writing the equation and is different than slope-intercept form.
Slope-intercept is the form you are used to: y = mx + b
y = (-3/5)x - (34/5) for the given example, as Orogogus showed how to get.
Standard form is different, though. It has to be in the form of Ax + By = C.
(3/5)x + y = 34/5
Both are equations of a line, and both can represent the same line. They're both really similar, so it just depends on how picky your teacher will get if (s)he will want you to specifically represent it in one form or the other. If it doesn't matter, then just stick with what you're doing and ignore everything I've said here for now.
3DS Friend Code: 3110-5393-4113
Steam profile
8- (x-2/2) = x/4
I tried starting out multiplying by two but that did not work, I tried getting rid of the fraction and that did not work and I have tried subtracting by 8 and that did not work. I am working it out like I would any other equation and it will not work, why is this one different?
I just got the answer but I do not know why it does not work any other way. To get the answer I multiplied everything by 4 and then divided the x-2 by 2 so now I have 32 -(2x-4) = x
32 - 2x +4 = x
36 = 3x
x=12
Was there any other way to do that?
Sorry I am reviewing the 9 sections I did over the weekend and I keep coming up with things I can not get the correct answer on.
I have to find the speed of a passenger train. A freight train takes 1 1/4 hours to get to the cirt and a passanger train averages 40 mph faster takes only 45 minutes to cover the same distance.
I get the equation .75x+40+1.25x = x
2x=-40
x=-20
Obviously that is not right, what am I doing wrong?
It looks like you've got your equation messed up a bit. How did you come up with the .75x + 40 + 1.25x = x?
For this I would set the two equal since they're traveling the same distance. So you want to solve for the passenger train speed, so that's x. The freight train speed is (x-40). .75x = the distance they're traveling, and so does 1.25(x-40). So you set those equal, .75x = 1.25(x-40). And then solve for x.
.75x = 1.25x - 50
.75x - 1.25x = -50
-.5x = -50
x = 100
For 8 - (x-2/2) = x/4, multiplying by 2 should have worked, except that it doesn't get you the whole way. Multiplying by 2 would give you 16 - (x-2) = x/2, or 18 = x/2 + x
18 = 3x/2
Problem is that here you need to multiply by 2 again to get
36 = 3x
x = 12
By multiplying by 4 you're avoiding the extra multiplication, but multiplying by 2 should work as a first step. Where did you run into problems when you multiplied by 2?
Another method, if you're interested.
Slope of a line when given two points is: y2-y1/x2-x1
-2-1/3--5
-(3/8) is the slope of your perpendicular line.
If you multiply the slopes of two lines which are perpendicular, you get -1. The easiest way to get this is to change the sign and flip the fraction.
-(3/8).X = -1
-(3/8).(8/3) = -1
Slopes are =-1 => slopes are perpendicular => 8/3 is slope you're looking for.
Uh, I'm not sure how clear this is, but I'm sure someone else can explain it better then me if you need it.
That method for the graph is a lot easier, I am going to write that down.