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- THE NEXT PROBLEM THAT I HAVE IS I WANT AN EQUATION
OF THE LINE THROUGH THE X-INTERCEPT
OF -5X + 3Y = 15 AND PARALLEL TO 2X - Y = 4.
WELL, NOTICE THAT NONE OF THE INGREDIENTS WAS GIVEN.
WE ARE NOT GIVEN THE SLOPE NOR THE POINT.
SO WE HAVE TO WORK FOR THEM, OKAY?
SO LET'S SEE.
THERE IS SOMETHING GIVEN HERE, THOUGH.
IT SAYS THAT THE LINE THAT I'M LOOKING FOR
GOES THROUGH THE X-INTERCEPT, WHICH IS A POINT, RIGHT,
OF THIS LINE.
AND ALSO, WE KNOW THAT THE LINE THAT WE WANT
IS PARALLEL TO THIS NEXT LINE, SECOND LINE.
LET'S LOOK AT OUR SCENARIO THAT WE HAVE HERE.
SO WE HAVE -5X + 3Y = 15 IS THIS LINE.
THE LINE THAT WE WANT
GOES THROUGH THE X-INTERCEPT OF -5X + 3Y = 15, OKAY?
2X - Y = 4 IS THIS LINE.
AND THE LINE IN QUESTION IS PARALLEL TO THIS LINE, OKAY?
SO THIS IS THE SITUATION THAT WE HAVE.
SO WE NEED TO SOLVE FOR THE X-INTERCEPT OF THE FIRST LINE.
AND RECALL THAT TO SOLVE FOR THE X-INTERCEPT OF A LINE
AND THE X-INTERCEPT, THE Y-COORDINATE IS 0.
SO ALL WE HAVE TO DO IS REPLACE THAT WITH 0
SO THAT TERM WILL DISAPPEAR, OKAY?
SO WE'LL GET -5X = 15,
AND DIVIDING THIS BY -5, WE GET X = -3.
AND THAT'S THE X-INTERCEPT IS (-3,0),
WHICH IS THE POINT THAT WE WILL USE FOR OUR LINE, OKAY?
NOW, FOR THE NEXT LINE, I WANT TO FIND THE SLOPE OF 2X - Y = 4.
SO I NEED TO WRITE THIS IN SLOPE INTERCEPT FORM,
WHICH MEANS I NEED TO ISOLATE MY Y, OKAY?
SO IF I WANT TO ISOLATE Y,
FIRST, I MOVE THE 2X OVER TO THE RIGHT SIDE.
SO I'LL GET -Y = -2X + 4.
SINCE Y IS NOT QUITE ISOLATED YET,
I HAVE TO MULTIPLY ACROSS THE BOARD BY -1
TO GET Y = +2X - 4, OKAY?
AND WE SEE THAT THE SLOPE OF THE GIVEN LINE IS 2.
THAT'S THE COEFFICIENT OF THE X, WHICH HAPPENS TO BE THE SAME
AS THE SLOPE OF THE LINE IN QUESTION, OKAY?
SO WE HAVE OUR INGREDIENTS.
WE HAVE A POINT AND THIS SLOPE, OKAY,
WHICH WE CAN PLUG IN OUR FORMULA,
LET ME JUST WRITE IT HERE.
SO Y - RY1 = 0, IS EQUAL TO M, WHICH IS 2, x X - -3, OKAY?
AND LET'S JUST SAY FOR--
WE WANT OUR SLOPE INTERCEPT FORM IN THIS CASE.
SO WE'LL GET Y EQUALS,
DISTRIBUTING THE 2, WE HAVE 2X - -3 IS +3.
SO 2 x +3 = +6.
AND THIS IS THE SLOPE INTERCEPT FORM OF THE LINE IN QUESTION.