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

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
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    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.

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  • March 20, 2013 at 6:25 am
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    Nice thank you very much

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  • April 24, 2013 at 2:56 pm
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    12,000th view!

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  • July 21, 2013 at 12:40 am
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    I really like your background. What software did you use?

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  • July 22, 2013 at 2:25 am
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    thank you sooooo much !!

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  • September 16, 2013 at 1:29 am
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    Thank you so much teach'.

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  • September 30, 2013 at 11:37 pm
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    thank you very much πŸ˜€

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  • November 1, 2013 at 11:41 am
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    Why didn't you so anything with the other 4 on the left side?

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  • November 1, 2013 at 11:42 am
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    So confused

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  • November 6, 2013 at 7:06 am
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    Thank you sooooo much!!!!

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  • November 27, 2013 at 7:26 am
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  • March 21, 2014 at 3:57 am
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    What program is this?

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  • May 22, 2014 at 4:37 am
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    Thank you, thank you so much for your help!!!!!

    Reply
  • August 6, 2014 at 7:41 pm
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    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 

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  • September 14, 2014 at 6:53 am
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    You are the best, thanks man.

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    your channel is helping me so much

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  • November 3, 2014 at 4:13 am
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    you teach better than most schools do tbh

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  • December 16, 2014 at 8:39 pm
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    Easier than any math teacher that taught me. Thank you

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  • May 12, 2015 at 1:31 am
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    thanks man thanks man thanks man thanks man thanks man that really helped!

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    this channel is a life saver

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  • August 14, 2015 at 12:30 pm
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    Brilliant! Thanks

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

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  • September 15, 2015 at 12:24 pm
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    thank you thank you thank you

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  • September 24, 2015 at 1:47 pm
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    Thank you so much! your far more capable than my teacher :)))

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  • September 29, 2015 at 5:16 pm
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    im following the instructions but its not working. my problem is 3x+4y=10 the points given are (5,8).

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  • October 1, 2015 at 3:58 am
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    Thank you so much 😭 I understand so much now.

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  • October 5, 2015 at 7:45 pm
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    Thank you very much. I have been struggling to "see" this and now I understand. And you gave both examples. !!!

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  • October 13, 2015 at 10:55 pm
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    Reply
  • October 23, 2015 at 1:27 am
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    God bless you, man. Thanks.

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  • October 28, 2015 at 7:49 pm
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    What happens if they are just ordered pairs and no slope give how would you do that?

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  • October 30, 2015 at 7:39 pm
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    OMG THANK U SOMEONE FINALLY CLEARLY EXPLAINED THIS. Thank you for saving my math grade lol

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  • November 11, 2015 at 10:19 pm
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    better than my teacher

    Reply
  • November 15, 2015 at 11:16 pm
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    Wait why did we disregard the 4? (y=-5x+4)

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  • November 17, 2015 at 1:47 am
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    Ohmygosh this video is such a great help

    Reply
  • November 30, 2015 at 3:13 am
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    Thank you for sounding human,
    all the other videos sound like robots lol
    this helped me alot!

    Reply
  • December 2, 2015 at 3:35 pm
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    this is so helpful

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  • December 3, 2015 at 12:41 am
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    Thank you!

    Reply
  • December 8, 2015 at 2:53 pm
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    Thank you so much

    Reply
  • December 9, 2015 at 11:05 pm
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    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?

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  • December 10, 2015 at 1:22 pm
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    Thank you.

    Reply
  • December 13, 2015 at 9:20 pm
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    thanks it was very helpful. its like life saver

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  • December 15, 2015 at 3:05 am
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    Thank you so much, this defiantly helped!

    Reply
  • January 4, 2016 at 5:37 am
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    thx so much 😊

    Reply
  • January 15, 2016 at 2:50 pm
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    Write an equation for the line parallel to the line βˆ’4x βˆ’ 3y = βˆ’1 through the point (6, βˆ’9). Please enter your answer in slope-intercept form or standard form. How would you solve this equation?

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  • January 22, 2016 at 4:29 am
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    thank you

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  • March 2, 2016 at 6:58 pm
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    Fantastic!

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  • March 3, 2016 at 5:10 pm
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    Thank you for captioning this

    Reply
  • March 24, 2016 at 10:16 am
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    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 ??

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  • June 8, 2016 at 3:02 pm
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    Thank you very much sir

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  • June 28, 2016 at 6:57 pm
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    i cried when i figured out how to do it then my clit settled down

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  • September 29, 2016 at 11:03 pm
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  • March 27, 2018 at 1:05 am
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    How do we know we add 4 to both sides 3:06

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    I have a test tommorow…

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  • September 30, 2019 at 1:40 am
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    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?

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