Ex 1: Find the Equation of a Line in Standard Form Given Two Points

Ex 1: Find the Equation of a Line in Standard Form Given Two Points


– WE WANT TO DETERMINE
THE EQUATION OF THE LINE PASSING THROUGH
THE GIVEN TWO POINTS, AND WE WANT THAT EQUATION
TO BE IN STANDARD FORM OR THE FORM WE SEE HERE. NOTICE HOW THE X AND Y TERMS
ARE ON THE LEFT SIDE, AND A, B, AND C
MUST BE INTEGERS. SO OUR STRATEGY
IS GOING TO BE TO FIRST FIND THE EQUATION
IN SLOPE INTERCEPT FORM, AND THEN CONVERT THE FORM OF
THE EQUATION TO STANDARD FORM. SO WE’RE ACTUALLY
GOING TO USE THE FORM Y=MX + B TO HELP US DETERMINE
THE EQUATION OF THE LINE WHERE WE KNOW IF WE HAVE TWO
POINTS ON THE LINE, THE SLOPE IS GOING TO BE=TO THE CHANGE IN THE Y
COORDINATES OR Y2 – Y1 DIVIDED BY THE CHANGE
IN THE X COORDINATES OR X SUB 2 – X SUB 1. SO IF THESE ARE OUR TWO POINTS, LETS GO AHEAD AND CALL THESE
THE 1s AND THESE THE 2s. SO THIS WILL BE X SUB 1,
THIS WILL BE Y SUB 1, THIS WILL BE X SUB 2,
AND THIS WILL BE Y SUB 2. SO LETS START BY DETERMINING
THE SLOPE OF THE LINE PASSING THROUGH
THESE TWO POINTS. THE SLOPE IS GOING TO BE EQUAL
TO Y SUB 2 – Y SUB 1. THAT’S 7 – 1 DIVIDED BY
X SUB 2 – X SUB 1, 1 – -1. THIS IS GOING TO BE 6 AND THIS
IS GOING TO BE 1 + 1 OR 2. SO THE SLOPE OF THE LINE=3. SO, AGAIN, REFERRING BACK
TO SLOPE INTERCEPT FORM, WE KNOW THE EQUATION
MUST BE Y=3X + B. SO WE STILL NEED TO DETERMINE
THE VALUE OF B OR THE Y INTERCEPT. AND WE CAN DO THAT BY SELECTING
ONE OF THESE TWO POINTS, AND SUBSTITUTING IN A VALUE
FOR Y AND X. SO FOR EXAMPLE, IF WE DECIDE
TO USE THIS POINT HERE, WE’D SUBSTITUTE 7 FOR Y,
1 FOR X, AND THEN WE CAN SOLVE FOR B. SO LETS GO AHEAD AND DO THAT. WE WOULD HAVE 7=3 x X
BUT X IS 1 + B, SO WE WOULD HAVE 7=3 + B. SO IF WE SUBTRACT
3 ON BOTH SIDES, WE CAN SEE THAT B=4. SO NOW BY SUBSTITUTING 4 FOR B, WE HAVE THE EQUATION
IN SLOPE INTERCEPT FORM. WE WOULD HAVE Y=3X + 4. BUT REMEMBER OUR ULTIMATE GOAL
IS TO HAVE THE EQUATION THE LINE IN STANDARD FORM, SO WE NEED THE X AND Y TERMS ON
THE LEFT SIDE OF THE EQUATION. SO TO DO THIS
WE’LL HAVE TO SUBTRACT 3X ON BOTH SIDES OF THE EQUATION. SO THIS WILL GIVE US
-3X + Y=4. NOW WE DO HAVE THE EQUATION
IN STANDARD FORM, BUT I DO WANT TO MENTION
THAT MANY TEXT BOOKS EXPRESS THE EQUATION OF A LINE
IN STANDARD FORM SO THAT THE X COEFFICIENT
IS POSITIVE. SO WE COULD MULTIPLY
EVERYTHING BY -1 TO PRODUCE AN EQUIVALENT
EQUATION WITH A POSITIVE COEFFICIENT
FOR X. AND LET’S JUST GO AHEAD
AND DO THAT. SO WE COULD ALSO EXPRESS
THIS EQUATION AS 3X – Y=-4. EITHER OF THESE EQUATIONS
ARE THE STANDARD FORM OF THE LINEAR EQUATION, BUT WE ALSO SHOULD RECOGNIZE THAT THEY ARE EQUIVALENT BECAUSE
IT COULD BE WRITTEN EITHER WAY. AND THE LAST THING
I DO WANT TO MENTION IN THIS VIDEO IS THAT A, B,
AND C DO HAVE TO BE INTEGERS. SO FOR EXAMPLE,
IF THE SLOPE WAS FRACTIONAL, WE WOULD HAVE TO CLEAR
THE FRACTIONS FROM THE EQUATION IN STANDARD FORM. AND WE’LL TAKE A LOOK
AT AN EXAMPLE LIKE THAT IN THE NEXT VIDEO.

9 thoughts on “Ex 1: Find the Equation of a Line in Standard Form Given Two Points

  • November 25, 2012 at 1:43 am
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    thank you so much, i've been struggling in my math class but im sure i can handle this now thank you.

    Reply
  • April 30, 2013 at 6:56 am
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    Thank you!

    Reply
  • October 19, 2013 at 7:38 pm
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    tnx man

    Reply
  • November 13, 2013 at 4:25 pm
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    Okay, I ended up with b = 0… Is that okay? @Mathispower4u 

    Reply
  • January 27, 2015 at 5:33 pm
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    i got lost in 2:17, why and how did he subtract -3?.. But still I learned more here than at school.. NICE!

    Reply
  • September 24, 2017 at 5:34 pm
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    Thanks so much man! I was having trouble in my math class until I found this video

    Reply
  • August 20, 2018 at 8:05 pm
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    I got 6+2y=2

    Is that right Im so lost

    Reply
  • July 30, 2019 at 4:27 pm
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    Thank you very much man! This was helpful even for someone who just finished a college algebra course.

    Reply
  • November 4, 2019 at 5:47 pm
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    Thank you so much dude

    Reply

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