-
Welcome to The Cave of Dragonflies forums, where the smallest bugs live alongside the strongest dragons.
Guests are not able to post messages or even read certain areas of the forums. Now, that's boring, don't you think? Registration, on the other hand, is simple, completely free of charge, and does not require you to give out any personal information at all. As soon as you register, you can take part in some of the happy fun things at the forums such as posting messages, voting in polls, sending private messages to people and being told that this is where we drink tea and eat cod.
Of course I'm not forcing you to do anything if you don't want to, but seriously, what have you got to lose? Five seconds of your life?
Homework Help Thread
- Thread starter Munchkin
- Start date
Scout
Imagine All Possibilities.
Ugh, I didn't feel like paying attention in class...
Line j is perpendicular to the line with the given equation and the line j passes through P. Write an equation of line j.
3.) 4x + 7y = 13, P(-2,6)
This might seem very easy to some, but my interest is not in math. I don't want others to only give the answers. Tell me how to do problems like this.
Line j is perpendicular to the line with the given equation and the line j passes through P. Write an equation of line j.
3.) 4x + 7y = 13, P(-2,6)
This might seem very easy to some, but my interest is not in math. I don't want others to only give the answers. Tell me how to do problems like this.
The key here is how perpendicular lines are related to one another. Specifically, they intersect one another at ninety-degree angles. In order to do so, their slopes have to be opposite reciprocals. You can show this by using geometry, but if you haven't done that yet, you can think of what you're doing as making the lines opposites of one another. If one line has a positive slope, then the other needs to have the opposite, or a negative slope. At the same time, if one line has a strongly positive slope, its opposite's negative is going to be weak, and vice versa. So, to make the slopes opposites, you first flip the sign on the slope, then flip the slope itself, turning it upside-down. A line with a slope of 1 is perpendicular to one with a slope of -1. A line with a slope of 2 is perpendicular to one with a slope of -1/2, and so on.
After that, you need to finish the equation so that the line also passes through the given point. Hopefully you've been taught that the general equation for a line is y = mx + b. You already have m, because that's the slope. You also have an x and y--those are the x and y values for the point you've been given. All you need to do at this point is plug the x and y you've been given into the general line equation, along with the slope you already found, and then solve to find b.
Dunno, there are no doubt people who could manage a much better explanation than that, but that's the method, anyway. I wasn't sure whether you wanted that problem done as an example or not, so I just wrote this in very general terms.
After that, you need to finish the equation so that the line also passes through the given point. Hopefully you've been taught that the general equation for a line is y = mx + b. You already have m, because that's the slope. You also have an x and y--those are the x and y values for the point you've been given. All you need to do at this point is plug the x and y you've been given into the general line equation, along with the slope you already found, and then solve to find b.
Dunno, there are no doubt people who could manage a much better explanation than that, but that's the method, anyway. I wasn't sure whether you wanted that problem done as an example or not, so I just wrote this in very general terms.
Last edited:
Right.
First, finding the slope of the original line.
4x + 7y = 13
y = -4x + 13
y = -4/7x + 13/7
The slope of the original line is therefore -4/7. Which means that the slope of the new line is going to be 7/4--flip the sign from negative to positive, then turn the fraction upside-down. The equation for the new line is thus far y = 7/4x + b.
Now plug in the point and solve for b, which is the y-intercept. The point we're given is (-2, 6).
6 = (7/4)(-2) + b
6 = -14/4 + b
6 + 14/4 = b
38/4 = b
19/2 = b
Plug that back into the equation, and you have the final answer: y = 7/4x + 19/2. To check your work, plug in six for y and see that you get -2 or plug in -2 for x and see that you get six for y.
Sorry, I messed up what I said in the earlier post--the slope is supposed to be the opposite reciprocal rather than just the opposite. I'll edit that explanation in in a moment.
First, finding the slope of the original line.
4x + 7y = 13
y = -4x + 13
y = -4/7x + 13/7
The slope of the original line is therefore -4/7. Which means that the slope of the new line is going to be 7/4--flip the sign from negative to positive, then turn the fraction upside-down. The equation for the new line is thus far y = 7/4x + b.
Now plug in the point and solve for b, which is the y-intercept. The point we're given is (-2, 6).
6 = (7/4)(-2) + b
6 = -14/4 + b
6 + 14/4 = b
38/4 = b
19/2 = b
Plug that back into the equation, and you have the final answer: y = 7/4x + 19/2. To check your work, plug in six for y and see that you get -2 or plug in -2 for x and see that you get six for y.
Sorry, I messed up what I said in the earlier post--the slope is supposed to be the opposite reciprocal rather than just the opposite. I'll edit that explanation in in a moment.
Last edited:
Minnow
If you're gonna dig, dig to the heavens!
Blegh. So, for Social Studies we have to do this research/brochure/thing on an American colony, and, knowing full well that it was owned by Massachusetts, I picked Maine. Basically I have to research stuffs about Maine (Government, History, Religion, Jobs/Economy, etc.) and it's proving impossible to find much of anything.
Does anyone know a good website to research about all that stuff?
Does anyone know a good website to research about all that stuff?
Minnow
If you're gonna dig, dig to the heavens!
Hmm. I'm getting plenty of info about Maine's history, but not much about actual goings-on in the 17th century, so I think I'll just go to the library tomorrow and find a book or three about Maine, and do my other homework I was planning to do tomorrow today.
Anyway, books seem to be a lot more helpful in this subject than Wikipedia and Google are being; I found loads of information in our school's encyclopedias.
Anyway, books seem to be a lot more helpful in this subject than Wikipedia and Google are being; I found loads of information in our school's encyclopedias.