Question

Find the equation of a line perpendicular to Y=5x+3. that passes through the point (-15,8)

Answer 1

Glad to have you as a new member of OpenStudy, LittleT! Welcome.

Given the line y=5x+3, find the slope of this line. call it m1.

To find the slope of a line perpendicular to the given line, take the negative reciprocal of m1.

Have you done that before? Call the result m2. m2 = ?

Answer 2

Thank you and this is the perpendicular proof right?

Answer 3

Not a proof, no. We're finding the slope of the given line, and then using it to find the slope of a line perpendicular to the given line.

Have you been able to identify m1?

Answer 4

@littlet?

Answer 5

Ok sorry. is M1 not y=5x+3?

Answer 6

See my private message. m1 is 5 alone. y=mx+b, where m=slope and b=y-intercept.

Answer 7

is m2 -5?

Answer 8

And yes i did see your message.

Answer 9

Given: m1=5

m2 is the "negative reciprocal" of m1.

This means you must first invert m1 to get 1 / m1, and then change the sign.

Start with m1=5.

Invert 5. Result?

Answer 10

-1/5

Answer 11

That's right. That's your m2.

Now you have the slope of a line perpendicular to the given line. You also have a point thru which the perpendicular line passes.

m2 = -1/5, and the point is (-15,8)

Answer 12

Pleae use the point-slope formula for the equation of a straight line to write the equation of the perpendicular line.

Answer 13

The point-slope formula is \[y-y _{0}=m(x-x _{_{0}})\]

Answer 14

Here your x0 = -15 and your y0=8

Answer 15

OK so x0 = -15 and your y0=8 is the equation in point-slope formula?

Answer 16

Not quite, LT. Start with \[y-y _{0}=m(x-x _{_{0}})\]

Answer 17

and substitute -15 for x0, and 8 for y0. Try it, please.

Answer 18

y-8=m(x- 15)

Answer 19

that right?

Answer 20

\[y-( ? ) = m*(x -( ? ) )\]

Answer 21

almost right. remember that x0 is -15. Have you taken that into account?

Answer 22

What is x-(-15)?

Answer 23

Yes sorry i ment -15

Answer 24

so you should end up with x+15. x-(-15)=x+15.

Answer 25

So now you have \[y-8=m(x+15)\]

Answer 26

ok

Answer 27

Pleae go back and find our value for m2.

Subst. that into the equation I've just shared with you.

Answer 28

m2 was -1/5 where would that go?

Answer 29

\[y-y _{0}=m2(x+15)\]

Answer 30

oh ok
so y- 8 = -1/5(x+15)

Answer 31

got to memorize that equation (point-slope form):\[y-y _{0}=m(x-x _{0})\]

Answer 32

Your result is perfect except that that -1/5 has to go inside parentheses for clarity.

Answer 33

\[so: y- 8 = -(1/5)(x+15)\]

Answer 34

alright got it. so tat is the solution?

Answer 35

This line goes thru the point (-15,8) and has a slope -1/5, which is the negative reciprocal of the slope of the given line.

Answer 36

Yes, that's the solution.

Answer 37

;)

Answer 38

Thank you so much!! have a great night!

Answer 39

You're welcome in more ways than one. Good night to you too (but it's only 3:23 p.m. here in California, where I live). See you again on OpenStudy!

Answer 40

Oh lol alright. Cya and thank you again
.

Answer 41

take care! Bye!