– 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.

thank you so much, i've been struggling in my math class but im sure i can handle this now thank you.

Thank you!

tnx man

Okay, I ended up with b = 0… Is that okay? @Mathispower4uÂ

i got lost in 2:17, why and how did he subtract -3?.. But still I learned more here than at school.. NICE!

Thanks so much man! I was having trouble in my math class until I found this video

I got 6+2y=2

Is that right Im so lost

Thank you very much man! This was helpful even for someone who just finished a college algebra course.

Thank you so much dude