Question

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

Answer 1

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

Answer 2

y=-5/2x +7

Answer 3

Perpendicular y=2/5x + 7/2

Answer 4

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?

Answer 5

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

Answer 6

Try that line again. Solving it for y, I mean.

I think you have a sign snafu. :)

Answer 7

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.

Answer 8

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).

Answer 9

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

Answer 10

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

Answer 11

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

That is step 1.

Answer 12

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

Answer 13

yes, good.

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

Answer 14

-5/2

Answer 15

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.)

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

Right - which gives you b = ?

Answer 20

b=-6

Answer 21

eek... no, double check. :)

Answer 22

my bad b=4

Answer 23

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?

Answer 24

the multiple choice answers come in a different format though

Answer 25

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

Answer 26

Standard form?

Ax + By = C ??

Answer 27

yeah

Answer 28

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.

Answer 29

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

Answer 30

Would it be 5x+2y=8

Answer 31

That looks right to me! :)

Answer 32

Thank you for helping

Answer 33

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