– WE WANT TO DETERMINE

THE EQUATION OF A LINE THAT IS PERPENDICULAR

TO Y=2X + 1, AND PASSES THROUGH THE POINT

WITH COORDINATES (-4,5). IF TWO LINES ARE PERPENDICULAR, THAT MEANS THEY INTERSECT

AND FORM A RIGHT ANGLE OR A 90 DEGREE ANGLE. AND IF TWO LINES

ARE PERPENDICULAR, THEN THEIR SLOPES ARE NEGATIVE

RECIPROCALS OF ONE ANOTHER, WHICH CAN BE WRITTEN

USING THIS NOTATION HERE, WHICH CAN BE

A LITTLE BIT CONFUSING. SO FOR EXAMPLE,

IF THIS FIRST LINE HAD A SLOPE OF LET’S SAY, 2/5, THEN THE SLOPE

OF THE SECOND LINE HERE WOULD HAVE TO BE

THE NEGATIVE RECIPROCAL, MEANING WE’LL FLIP THIS OVER

AND THEN CHANGE THE SIGN. SO IT’S GOING TO BE -5/2. OKAY, SO BACK TO OUR PROBLEM, WE WANT A LINE THAT IS

PERPENDICULAR TO Y=2X + 1. WELL, THIS LINE

IS IN SLOPE INTERCEPT FORM, SO WE SHOULD RECOGNIZE THAT

THE SLOPE OF THIS LINE IS 2/1. THEREFORE, THE SLOPE

OF THE PERPENDICULAR LINE WOULD BE THE NEGATIVE RECIPROCAL

OF THIS. SO FOR THE SLOPE OF OUR LINE, WE’LL HAVE TO FLIP THIS OVER

AND CHANGE THE SIGN. THAT WOULD GIVE US -1/2. -1/2 IS A NEGATIVE RECIPROCAL

OF 2/1. AND THEN WE KNOW OUR LINE ALSO

PASSES THROUGH THE POINT (-4,5). NOW, TO DETERMINE THE EQUATION

OF THE LINE WITH SLOPE OF -1/2 CONTAINING THE POINT (-4,5), WE CAN EITHER USE

SLOPE INTERCEPT FORM, OR THE POINT SLOPE FORM

OF THE LINE. AND I THINK FOR THIS VIDEO

WE’LL SHOW BOTH. SO USING JUST SLOPE INTERCEPT

FORM OR THE FORM Y=MX + B, WE WOULD FIRST SUBSTITUTE -1/2

FOR M. SO WE’D HAVE Y=-1/2X + B. AND THEN TO DETERMINE

THE Y INTERCEPT, IT’S NOT GOING TO BE +5 BECAUSE

THE X COORDINATE IS NOT ZERO. BUT SINCE THIS POINT

IS ON THE LINE THAT MEANS IF WE SUBSTITUTE

THESE COORDINATES INTO THE EQUATION IT SHOULD SATISFY THE EQUATION. SO WE’LL SUBSTITUTE -4 FOR X,

5 FOR Y, AND THEN SOLVE FOR B. SO WE’D HAVE 5=-1/2 x -4 + B. PUT THAT -4/1

SO WE HAVE 5 EQUALS– AND SO THIS SIMPLIFIES HERE,

THERE’S ONE 2 IN 2, AND TWO 2s IN 4. THIS BECOMES -1 x -2. DON’T FORGET

ABOUT THE SIGN HERE. SO NOW IF WE SUBTRACT 2

ON BOTH SIDES– WE HAVE B EQUALS–

THIS WILL BE +3. SO NOW WE HAVE OUR EQUATION, AND

WE’LL JUST SUBSTITUTE +3 FOR B. AND THE EQUATION WILL BE

Y=-1/2X + 3. AND LET’S GO AHEAD AND SEE

IF WE CAN GET THE SAME EQUATION USING POINT SLOPE FORM. POINT SLOPE FORM OF A LINE IS

Y – Y1=M(X – X SUB 1), WHERE M IS THE SLOPE, AND (X SUB 1,Y SUB 1)

IS A POINT ON THE LINE. SO FOR THIS SITUATION

X SUB 1 IS GOING TO BE -4, AND Y SUB 1 WILL BE +5. SO WE’D HAVE Y – 5=-1/2(X). NOW, HERE WE’D HAVE MINUS -4,

WHICH IS THE SAME AS +4. AND NOW WE’LL GO AHEAD

AND SOLVE THIS EQUATION FOR Y. SO WE’LL DISTRIBUTE HERE, SO WE’LL HAVE Y – 5=

THIS WOULD BE -1/2X. THEN HERE WE’D HAVE -2, AND THE LAST STEP TO SOLVE FOR Y

WOULD BE TO ADD 5. THIS WOULD BE 0,

SO WE’D HAVE Y=-1/2X, AND THIS WILL BE +3. SO NOTICE HOW IF WE JUST USE

SLOPE INTERCEPT FORM TO DETERMINE THE EQUATION, OR IF WE USE POINT SLOPE FORM

TO DETERMINE THE EQUATION, THE RESULT IS THE SAME. AND LET’S GO AHEAD AND QUICKLY

VERIFY THIS GRAPHICALLY. YOU WERE GIVEN THE RED LINE

Y=2X + 1, AND WE DETERMINED

THAT THE EQUATION OF THE PERPENDICULAR LINE

WAS Y=-1/2X + 3. NOTICE HOW THESE TWO LINES DO

INTERSECT IN A RIGHT ANGLE HERE, AND THE BLUE LINE DOES CONTAIN

THE GIVEN POINT THAT HAD A COORDINATES (-4,5),

THIS POINT HERE. SO OUR WORK LOOKS GOOD. I HOPE YOU FOUND THIS HELPFUL.

Thank you soo much! You literally saved my life! My gratitude for posting this video <3

Thank you

Thank you, Yes I can finish my work!

5:00

Perfect for tomorrows test!

thxs

Thank u so much

I need some engineering analytic geometry sir 🙂 pls upload some

Thanks

Thank You, you saved my math grade!

thanks

Holy shiz THANKS…

Thank you so much! Need this for the NYS Regents!

THANK YOU got maths gcse monday :((((

This was so helpful. Thank you~~

OMG THANKS A BUNCH MATE !!!!!!!!! Love you, no homo <3

Thank you so very much!

THANK YOU SO MUCH!!!!

Do u not need to do anything with the one

OMFG THANK YOU SOOOOOOOOO MUCH!!!!!!!!!!!!!!!!!!!

Thanks! Great help.

Thanks! You helped me so much… You are a really good explainer.

how did you get 3 on the first method when the difference between 5 and -2 is 8

My GCSE exam is in less than 9 hours. Thank you so much.

Well, since everyone is saying thanks….

THANKS! I'm taking Algebra II next year and i don't remember this AT ALL!

Thanks very much!

Great video!

wish u were my math professor..

Thank you very much. It was really very helpful

Doing a review sheet currently and thus really helped me out thanks!

Great video, look forward to seeing more! You helped me understand the concept a lot better, thanks for the help b4 my test!

thank you dear

I like how most of the people using this video are in highschool of college, I'm in 7th grade advanced algebra😂😂

What would u do if they only gave u x and the points

Thanks very helpful.

thank you for this my final is tomorrow and i was so stuck so helpful

Thanks so much this helped me a lot

Yo yo good lookin out playa

great video and big help! thank you

thanks helped out a lot

This was really helpful thanks so much

Thank you so much for this video! The clear and concise explanations were extremely helpful.

Thank you!

Brilliant video!

Thank you for captioning this

we appreciate you

Thankyouuu. Its very helpful.

This was helpful.

great video, very helpful.

but what if the two fractions cannot simplify?

Very helpful, thanks 🙂

thanks a lot 😍😍

This was helpful

Wow great video man! Thank you!!

to boring to watch ! had to repeat this video 6 times lol

You've raised my grade from a 60 to a 90!! thanks alot!!! I understand this!

Awesome video, loved it! Thank you, this really helped me study for tomorrows test

Thank you that video it's very greatful…..yeah…

3:00 What About The +1???

Thank you, such a life saver 😊

Bro thanks

if only i saw this a day earlier

.. i messed up a test at school, and now i am depressed..

You sir are my god and saviour

Thanks! I have an exam soon and I'm so confused about most of the Linear section.

Very neat + easy explanation!! Thanks a lot for posting this 🙂

Thanks , good method helped me out!

You da real MVP

thank you so much

Please send me emails of the videos. Im stuck at school.

thank you so much I was overthinking this way too much

thx

Thnks

THANK YOU SO MUCH AND HAPPY NEW YEAR 2018!!!

Thx so much

thanks man !

thank you I was struggling on my homework and now I got it thank you again !

very helpful

Thx a ton bro, maths can get so hard sometimes

This is soooo helpful for my upcoming math unit 6 secondary 1 test tomorrow! All the visuals really make more sense all laid out.

There's just one thing I dont get, isnt this the same as finding a parellel line equation?

yes!!

what if its -8x will the reciprocal be -1/8x or 1/8x? someone help PLEASE!! have to prepare for a test

its awesome

Super helpful. Thanks!!!

Not enough explanation lol

I'm taking algebra this year and I'm about to cry in class because the teacher says a bunch of useless information like foods and his family……

THANK YOU SOOOOOOOOO MUCH for this video!

Thank you

Thanks

thank you so much .

Help!

Write an equation in slope intercept form for the line that

passes through the given point and is perpendicular to the graph of the

equation.

(-2,3),y=-1/2x-4

thx bro that helped a lot for midterms!!

Thanks for this video.

I got an a+++++-+—+ from this thanks 🙏

what if the slope is 1? would you just use -1?

Thank you so much

Once again, YouTube has taught be better than my own teacher!

Thanks 🙏

the internet is going to be the new school. prediciton 2030

thank you, ill use this for programming algorithm

THANK YOU SO MUCH YOU SAVED ME