Find an equation. Write the equation using function notation

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LMande

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Find an equation for the line through (-4, 8) and perpendicular to 2x - 3y = 1. Write the equation using function notation.

I'm going to take a shot and say the first step is to find the slope???

-3y = 2x + 1
y = -2x/-3 +1

I have no idea what I'm doing here. Any help? Suggestions? Eeek!
 
You have the slope. m = (-2)/(-3) = 2/3

What is the slope of the perpendicular?
 
I got the perpendicular part. Thanks, but now what? I guess I'm not even sure what they're asking here.
 
It's a quiz about definitions. You should know two things:

1) Parallel lines have the SAME slope.
2) Perpendicular lines - Multiply the slopes and get -1.

In your case, you have m=2/3, and you want m=-3/2

Now you have a point and a slope. You should be able to write down the equation of such a line.
 
tkhunny said:
It's a quiz about definitions. You should know two things:

1) Parallel lines have the SAME slope.
2) Perpendicular lines - Multiply the slopes and get -1.

In your case, you have m=2/3, and you want m=-3/2

Now you have a point and a slope. You should be able to write down the equation of such a line.
Click to expand...

So since we know a point and slope use point slope form and convert it into function notation.

............Point slope form: \(\displaystyle \L \;y-y_1\,=\,m(x-x_1)\)

The \(\displaystyle m\) is your slope and \(\displaystyle x_1\;&\;y_1\) are the coordinates you know.
 
Still lost..

Jonboy are you saying that the point slope form is the answer?
 
Given any line Ax+By=C then Bx-Ay=D is perpendicular to it.
So given 2x-3y=1 the line you want is 3x+2y=D.
How do you find D?
Well (-4,8) is on that line. So 3(-4)+2(8)=D.
 
Re: Still lost..

LMande said:
Jonboy are you saying that the point slope form is the answer?
Click to expand...

No I am saying get your equation in point slope form and then get it in function notation.
 
I'm think I'm even more confused now.

I'm sorry. You guys must hate it when someone as ignorant as I am comes on to this site. See, my problem is that my instructor teaches one way. The lecturer another, and the book yet another way. I've posted a message for some help from my instructor and will see what it is she's looking for. Is there anyone out there that can break this down for me?
 
Look the answer is \(\displaystyle y = \frac{{ - 3}}{2}x + 2.\)
That is not giong to help you at all unless you understand how to get for yourself.
 
LMande said:
Is there anyone out there that can break this down for me?
Click to expand...
The problem has been "broken down" for you; it's even been (almost) completed for you.

It might help if you showed what you have done, so the tutors could try to figure out where you're having trouble. Right now, having pretty much given you the answer, it would be understandable if they found it difficult to see what else you might need.

Thank you.

Eliz.
 
pka and stapel

I understand your frustrations and my sincerest apologies. I guess I just get confused and overwhelmed when I see all the different responses and questions of me. I'm not trying to be difficult. I thought I was clear in what I said I understood and that is what I believed the first step to be. Find the slope (which I think I did). I also understand that since it's perpendicular that it would be opposite.

Which I understand where he gets -3/2x as the slope. Now I see that he has:

y= -3/2x +2. How did he get the +2? I'm not fishing for answers here guys.

I truly am just trying to understand how this works.
 
Re: I'm think I'm even more confused now.

LMande said:
You guys must hate it when someone as ignorant as I am comes on to this site.
Click to expand...
I understand your frustrations and my sincerest apologies.
Click to expand...
Why don't you let us worry about all this. You just keep doing your best.

Most fundamentally, you should have a couple of tools in your pocket. One such tool is a better understanding of lines. Lines need two pieces of information. For each two pieces of information, there is a "form" that will allow you simple to write down the equation of a line. Here's three of them:

Point-Slope
2-Point
Intercept

Personally, I like the third one, but it is used only rarely. Find the other two in your book or in your lecture notes. Stare at them until you get it. You simply must know what the "point-slope" form and the "2-point" form do for you.

Along with this, you simply must know how to express a point in an xy-plane. It's usually like this, (x,y).

After knowing how to communicate a point's address, and after internalizing the point-slope and 2-point forms, there are many, many questions that can be asked, most going to a little effort to disguize what they are telling you. This is the problem you have. You have a point simply given to you, (-4,8). You have only a hint for the slope. The word "perpendicular" is your hint. That's where -3/2 came from. Now we have a point and a slope. Just plug it in the point-slope form.

If you don't understand the point-slope form, you can't do this problem and it should not be expected of you.

If you don't know the relationship between slopes of perpendicular lines, you can't do this problem and it should not be expected of you.
 
Re: I'm think I'm even more confused now.

LMande said:
Is there anyone out there that can break this down for me?
Click to expand...

Fill in your x and y coordinate into point slope form:


\(\displaystyle \L y\,-\,8\,=\,-\,\frac{3}{2}(x\,+\,4)\,\to\, y\,-\,8\,=\,-\frac{3}{2}x\,-\,6\,\to\,y\,=\,-\,\frac{3}{2}x+2\)

...............

So change the y to \(\displaystyle f(x)\) and -- voila! -- function notation (this is a rule): \(\displaystyle \L f(x)\,=\,-\,\frac{3}{2}x\,+\,2\)
 
Re: Find an equation. Write the equation using function nota

LMande said:
Find an equation for the line through (-4, 8) and perpendicular to 2x - 3y = 1. Write the equation using function notation.

I'm going to take a shot and say the first step is to find the slope???

-3y = 2x + 1
y = -2x/-3 +1

I have no idea what I'm doing here. Any help? Suggestions? Eeek!
Click to expand...
Well, to start, that's wrong; should be:
3y = 2x - 1
y = (2/3)x - 1/3
 
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