# Ex 1: Find the Equation of a Line Parallel to a Given Line Passing Through a Given Point

– WE WANT TO DETERMINE
THE EQUATION OF THE LINE THAT IS PARALLEL TO Y=-5X + 4
AND PASSES THROUGH THE POINT WITH COORDINATES (-1,4). THE MAIN THING TO REMEMBER HERE
IS THAT IF LINES ARE PARALLEL, AS WE SEE HERE ON THE RIGHT, THE
SLOPES ARE EQUAL TO EACH OTHER. SO IF WE WANT A LINE
THAT IS PARALLEL TO Y=-5X + 4, THE SLOPE OF THE NEW LINE
MUST BE -5 AND IT PASSES THROUGH
THIS POINT. SO NOW WE NEED TO FIND
THE EQUATION OF A LINE WITH A SLOPE OF -5
THAT CONTAINS THE POINT (-1,4). NOW, THERE ARE TWO MAIN WAYS
OF DETERMINING THE EQUATION OF A LINE
GIVEN THE SLOPE AND A POINT. WE CAN USE JUST SLOPE INTERCEPT
FORM, WHICH IS Y=MX + B OR WE COULD USE
POINT SLOPE FORM, WHICH IS
Y – Y1=M(X – X SUB 1). I’M GOING TO GO
AND SHOW THIS BOTH WAYS. SO IF WE USE SLOPED INTERCEPT
FORM WE CAN SUBSTITUTE -5 FOR M. SO WE’D HAVE Y=-5X + B, BUT WE STILL NEED TO DETERMINE
THE Y INTERCEPT. AND THIS Y COORDINATE
IS NOT THE Y INTERCEPT BECAUSE X IS NOT=0, BUT THIS POINT IS ON THE LINE SO
WE CAN SUBSTITUTE THESE VALUES INTO THE EQUATION
AND THEN SOLVE FOR B. SO WE’LL SUBSTITUTE -1 FOR X AND
POSITIVE 4 FOR Y TO DETERMINE B. SO WE’D HAVE 4=-5 x -1 + B. SO WE HAVE 4=5 + B. SO NOW WE’LL SUBTRACT 5
ON BOTH SIDES TO SOLVE FOR B. SO WE HAVE B=-1. SO NOW WE CAN SUBSTITUTE -1
FOR B INTO THIS EQUATION HERE AND WE HAVE THE EQUATION
IN SLOPE INTERCEPT FORM. WE WOULD HAVE Y=-5X AND
THEN + -1 IS EQUIVALENT TO – +1. SO THIS WOULD BE OUR EQUATION
IN SLOPE INTERCEPT FORM. AND I’LL SEE IF WE GET
THE SAME EQUATION IF WE USE
POINT SLOPE FORM INSTEAD. REMEMBER IN POINT SLOPE FORM
M IS STILL THE SLOPE, BUT X SUB 1, Y SUB 1 ARE THE CORNERS OF ANY POINT
ON THE LINE. SO WE’LL USE -1 FOR X SUB 1
AND 4 FOR Y SUB 1. SO WE WOULD HAVE Y – 4=-5(X). AND THEN HERE WE’D HAVE – -1,
WHICH IS EQUIVALENT TO 1. AND NOW TO WRITE THIS
IN SLOPE INTERCEPT FORM WE’LL SOLVE FOR Y
SO WE’LL DISTRIBUTE HERE. SO WE’D HAVE Y – 4=-5X – 5
AND THEN WE ADD 4 TO BOTH SIDES, THIS WOULD BE ZERO. AND YOU CAN SEE WE’RE GOING TO
HAVE THE SAME EQUATION. WE’LL HAVE Y=-5X
AND THEN THIS IS -1. SO AS YOU CAN SEE
WHICHEVER METHOD YOU USE THE RESULT IS THE SAME. IT JUST DEPENDS ON WHAT METHOD
YOU WANT TO USE. LET’S GO AHEAD
AND QUICKLY VERIFY THAT THIS LINE IS PARALLEL
TO THE GIVEN LINE AND CONTAINS THE POINT (-1,4). RIGHT AWAY WE CAN SEE
THEY HAVE THE SAME SLOPE SO THEY ARE PARALLEL. THE GIVEN EQUATION PRODUCED
THE RED LINE AND THE EQUATION THAT WE FOUND
PRODUCED THE BLUE LINE. NOTICE HOW THE BLUE LINE DOES CONTAIN THE POINT (-1,4)
RIGHT HERE. HAS THE SAME SLOPE
AS THE RED LINE, WHICH WAS -5 AND IT DOES HAVE
A Y INTERCEPT OF -1. SO THIS VERIFIES
OUR WORK IS CORRECT.

### 100 thoughts on “Ex 1: Find the Equation of a Line Parallel to a Given Line Passing Through a Given Point”

• March 15, 2013 at 1:30 am

The y-intercept is (0,b). The given point on the line is (-1.4). Notice the y-coordinate is 4, but this is not the y-intercept since the x-coordinate in not 0. This is a common error.

• March 20, 2013 at 6:25 am

Nice thank you very much

• April 24, 2013 at 2:56 pm

12,000th view!

• July 21, 2013 at 12:40 am

I really like your background. What software did you use?

• July 22, 2013 at 2:25 am

thank you sooooo much !!

• September 16, 2013 at 1:29 am

Thank you so much teach'.

• September 30, 2013 at 11:37 pm

thank you very much π

• November 1, 2013 at 11:41 am

Why didn't you so anything with the other 4 on the left side?

• November 1, 2013 at 11:42 am

So confused

• November 6, 2013 at 7:06 am

Thank you sooooo much!!!!

• November 27, 2013 at 7:26 am

THANK YOU SOOOO MUCH!!!! HELPED ME SOOOOO MUCH <3 <3 π π π π

• March 21, 2014 at 3:57 am

What program is this?

• May 22, 2014 at 4:37 am

Thank you, thank you so much for your help!!!!!

• August 6, 2014 at 7:41 pm

I have the same problem, (8,10) for the points but for the y-intercept I have y= 8/3x+7. I'm really bad at fractions, how would I solve this?Β

• September 14, 2014 at 6:53 am

You are the best, thanks man.

• November 3, 2014 at 4:12 am

your channel is helping me so much

• November 3, 2014 at 4:13 am

you teach better than most schools do tbh

• December 16, 2014 at 8:39 pm

Easier than any math teacher that taught me. Thank you

• May 12, 2015 at 1:31 am

thanks man thanks man thanks man thanks man thanks man that really helped!

• June 10, 2015 at 11:04 pm

this channel is a life saver

• August 14, 2015 at 12:30 pm

Brilliant! Thanks

• September 11, 2015 at 10:31 pm

Saved my grade!I really understood well!!! you are the best

• September 15, 2015 at 12:24 pm

thank you thank you thank you

• September 24, 2015 at 1:47 pm

Thank you so much! your far more capable than my teacher :)))

• September 29, 2015 at 5:16 pm

im following the instructions but its not working. my problem is 3x+4y=10 the points given are (5,8).

• October 1, 2015 at 3:58 am

Thank you so much π­ I understand so much now.

• October 5, 2015 at 7:45 pm

Thank you very much. I have been struggling to "see" this and now I understand. And you gave both examples. !!!

• October 13, 2015 at 10:55 pm

thank god for this channel

• October 23, 2015 at 1:27 am

God bless you, man. Thanks.

• October 28, 2015 at 7:49 pm

What happens if they are just ordered pairs and no slope give how would you do that?

• October 30, 2015 at 7:39 pm

OMG THANK U SOMEONE FINALLY CLEARLY EXPLAINED THIS. Thank you for saving my math grade lol

• November 11, 2015 at 10:19 pm

better than my teacher

• November 15, 2015 at 11:16 pm

Wait why did we disregard the 4? (y=-5x+4)

• November 17, 2015 at 1:47 am

Ohmygosh this video is such a great help

• November 30, 2015 at 3:13 am

Thank you for sounding human,
all the other videos sound like robots lol
this helped me alot!

• December 2, 2015 at 3:35 pm

• December 3, 2015 at 12:41 am

Thank you!

• December 8, 2015 at 2:53 pm

Thank you so much

• December 9, 2015 at 11:05 pm

Now if the equation says y=x-8, would I write that as y=x-b or y=x+b when folowing the first step?

• December 10, 2015 at 1:22 pm

Thank you.

• December 13, 2015 at 9:20 pm

thanks it was very helpful. its like life saver

• December 15, 2015 at 3:05 am

Thank you so much, this defiantly helped!

• January 4, 2016 at 5:37 am

thx so much π

• January 15, 2016 at 2:50 pm

Write an equation for the line parallel to the line β4x β 3y = β1 through the point (6, β9). Please enter your answer in slope-intercept form or standard form. How would you solve this equation?

• January 22, 2016 at 4:29 am

thank you

• March 2, 2016 at 6:58 pm

Fantastic!

• March 3, 2016 at 5:10 pm

Thank you for captioning this

• March 24, 2016 at 10:16 am

so when you use the equation y=-5x+4 , you dont do anything with the +4 ? you only use the slope and the point ? so you just basically dont pay attention to the +4 am i right ??

• June 8, 2016 at 3:02 pm

Thank you very much sir

• June 28, 2016 at 6:57 pm

i cried when i figured out how to do it then my clit settled down

• September 29, 2016 at 11:03 pm

Thank you so muchhh! π

• October 6, 2016 at 7:57 pm

I probably would have failed geometry if it wasn't for you guys LOVE YA!!

• October 6, 2016 at 8:23 pm

Thank You!!!

• December 1, 2016 at 6:50 pm

thanks so much! this was very helpful

• December 4, 2016 at 11:47 pm

My Algebra grade would've dropped from an A to a D if it weren't for this video!! Thank you!

• February 15, 2017 at 11:58 pm

Gotta say, I'm learning this right now in school, I missed the day where the teacher explained it, and I have a test the next day. This saved my life!!!!

• February 16, 2017 at 5:03 am

thanks!!

• March 25, 2017 at 4:25 am

what the fuck, i think i might have understood maths

• April 3, 2017 at 9:06 pm

Thank you so much! This was very helpful. Hopefully I do well on my quiz tomorrow! πππΎ

• May 2, 2017 at 5:09 pm

Why does sometimes Youtube teach better than School

• May 18, 2017 at 2:38 am

dude you're the best

• May 29, 2017 at 7:05 pm

I do wish you'd stop smacking your lips against the mic. It's REALLY distracting.

• August 27, 2017 at 7:15 pm

thank you so much :3

• August 31, 2017 at 1:31 pm

Thank you again!!!

• October 25, 2017 at 10:44 pm

Thank you so much this is amazing

• November 1, 2017 at 10:25 pm

Thank you!!!!!!!

• November 12, 2017 at 7:44 pm

THANK YOU!!!!!!!!!!!!!!

• November 21, 2017 at 7:20 pm

You are my math hero

• December 20, 2017 at 4:18 am

This was very clear and understanding thank you

• January 14, 2018 at 5:25 pm

U have just saved me, I have an exam tomorrow and this vid had genuinely just saved me, thanks soooo much

• January 24, 2018 at 1:48 am

This is so much easier now that i understand it! Thank you so much!

• January 27, 2018 at 5:21 pm

thank you!!

• March 3, 2018 at 12:35 am

bro ur a god in the maths worldπππ^_^^_^^_^^_^^_^^_^^_

• March 27, 2018 at 1:05 am

How do we know we add 4 to both sides 3:06

• June 3, 2018 at 10:58 am

Thank you dude, if your channel is all maths formulas, imma subscribe.

• June 5, 2018 at 11:06 am

Thank u sooooo much

• August 25, 2018 at 2:25 am

Thnks alot

• August 28, 2018 at 5:40 am

• September 15, 2018 at 8:12 pm

Thank you so much, I'm finally understanding this concept,my teacher sucks

• September 19, 2018 at 1:24 am

Dont understand why this has any dislikes at all. Thank you so much!

• October 16, 2018 at 2:41 am

THX

• October 18, 2018 at 11:59 pm

π

• November 3, 2018 at 7:23 pm

thank you u litteraly teach better than my advanced math class teacher

• November 13, 2018 at 11:45 pm

Only 30 seconds in and I understand my math so much better already.

• November 26, 2018 at 1:41 am

Fuck math

• December 2, 2018 at 1:05 pm

Subscribed

• December 2, 2018 at 1:05 pm

Youve earned my respect

• December 4, 2018 at 9:25 pm

If there were a way to graph my shift of motivation, it would have a slope of 1 million. Hahaha thank you!!! So helpful.

• December 13, 2018 at 4:01 am

LIFESAVER π

• March 23, 2019 at 8:40 pm

Yo why'd u sound like u don't wanna teach

• March 24, 2019 at 9:36 am

I have a test tommorow…

• September 30, 2019 at 1:40 am

What we do if the equation is x+24=-5 and the point is (1,2)? How do we solve this if we do not have a y?

• November 1, 2019 at 3:26 am

Got a geo test tmrw and this rlly helped. Even 8 years later, thanks bud.

• November 2, 2019 at 11:23 pm

his voice has a calming effect, and that's saying something because usually I hate math (srry math lovers)

• November 6, 2019 at 2:58 pm

Thanks

• November 12, 2019 at 3:00 pm

what a legend