Write the equation for the line through the point P(2,-1) that is perpendicular to the line 2x-5y=7

- anonymous

Write the equation for the line through the point P(2,-1) that is perpendicular to the line 2x-5y=7

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- katieb

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- DebbieG

Do you know how to find the slope of the line 2x-5y=7?

- anonymous

y=-5/2x +7

- anonymous

Perpendicular y=2/5x + 7/2

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## More answers

- DebbieG

Wait a sec. I'm not sure what you're telling me.
Do you know the slope of the line, 2x-5y=7 which is perpendicular to the line you are looking for?

- anonymous

2x-5y=7 is y=(-5/2)x + 7/2
when the equation is perpendicular it is y=(2/5)x + 7/2

- DebbieG

Try that line again. Solving it for y, I mean.
I think you have a sign snafu. :)

- DebbieG

In the meantime, let's talk about the perpendicular line. Once you have the correct slope for the given line, you do have the right idea, in that the perpendicular line has, as its slope, the NEGATIVE RECIPROCAL of the other line.
That is, if r/p is the slope of Line 1, then -p/r is the slope of any line perpendicular to Line 1.
But you used, as your y-intercept, the same y-intercept is the first line?? That is not (necessarily) correct.

- DebbieG

Once you have the correct slope, you need to use the GIVEN POINT P(2,-1) to find the equation for the perpendicular line.
You'll have the slope. And you have a point on the line. From those, you can get the equation for the line (either use point-slope form, or solve y=mx+b for b, either will work).

- anonymous

would 2x-5y=7 be 2x+5y=7?

- DebbieG

No, those are different...?? I'm not sure what you mean.

- DebbieG

To find the slope of the given line, 2x-5y=7, just solve for y. You did that incorrectly above.
That is step 1.

- anonymous

For 2x-5y=7 the slope is 2/5

- DebbieG

yes, good.
So the perpendicular line, which you are looking for, has slope = ?

- anonymous

-5/2

- DebbieG

Right. So you have slope, m=-5/2. You have a point on the line, (2, -1). How do you find the equation of a line, given the slope and a point on the line? (There are at least a couple of ways to do this, so more than one right answer here.)

- anonymous

-1=(-5/2) + b ?

- DebbieG

Oops, you forgot something in there. Do you see what? Just double check it.

- anonymous

-1=(-5/2)(2) + b

- DebbieG

Right - which gives you b = ?

- anonymous

b=-6

- DebbieG

eek... no, double check. :)

- anonymous

my bad b=4

- DebbieG

That's it! :) So you have the slope and now you have the y-intercept, so you know how to write the equation for the line... right?

- anonymous

the multiple choice answers come in a different format though

- DebbieG

By the way, you can always do an "intuition check" of a problem like this by graphing the 2 lines on a graphing calculator, or using an internet graphing tool like Wolfram. It does not GUARANTEE that your answer is correct, but if the lines look WAAAAAY off from perpendicular, you might be able to tell. Seeing the and being able to tell that they "appear to be" perpendicular can give you a sense of confidence about your answer:
http://www.wolframalpha.com/input/?i=y%2B1%3D%28-5%2F2%29%28x-2%29+and+2x-5y%3D7

- DebbieG

Standard form?
Ax + By = C ??

- anonymous

yeah

- DebbieG

Just switch the form of the equation. You'll put the x & y terms on the LHS, then multiply by whatever you need to to eliminate the den'r. I'll do a DIFFERENT example for you:
y=(-2/7)x + 1
To put in standard form: I'll add (2/7)x to both sides:
(2/7)x + y = 1
Now I need integer coefficients. So multiplying both sides by 7 will take care of that:
7*[(2/7)x + y ]= 1*7
2x+7y=7
Tah-dah! Standard form.

- DebbieG

And in standard form, we always make sure that A (the coefficient on x) is positive.

- anonymous

Would it be 5x+2y=8

- DebbieG

That looks right to me! :)

- anonymous

Thank you for helping

- DebbieG

you're welcome. :) good work, sticking to it! :)

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