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- WE WANT TO DETERMINE THE EQUATION OF THE LINE
AND WE WANT THE LINEAR EQUATION TO BE IN SLOPE INTERCEPT FORM,
WHICH IS THE FORM Y = MX + B
WHERE M IS THE SLOPE OF THE LINE AND B IS THE Y INTERCEPT.
AND JUST TO REVIEW, THE SLOPE
IS OFTEN DEFINED AS THE RATIO OF THE RISE TO THE RUN,
WHICH IS THE RATIO OF THE VERTICAL CHANGE
TO HORIZONTAL CHANGE
OFTEN DENOTED AS THE RATIO OF THE CHANGE IN Y
TO THE CHANGE IN X.
AND B IS THE Y INTERCEPT.
AND WE CAN DETERMINE BOTH OF THESE BY ANALYZING THE GRAPH.
TO DETERMINE THE SLOPE, IF WE SELECT 2 POINTS ON THIS LINE
WITH INTEGER COORDINATES
WE SHOULD BE ABLE TO DETERMINE THE SLOPE.
SO FOR EXAMPLE, IF WE SELECT THIS POINT HERE
THAT HAS COORDINATES (3,3)
AND THIS POINT HERE THAT HAS COORDINATES (6,5)
WE SHOULD BE ABLE TO DETERMINE THE RATIO OF THE CHANGE OF Y
TO THE CHANGE IN X.
SO FOR EXAMPLE, IF WE MOVE FROM THIS POINT TO THIS POINT
NOTICE HOW WE'D HAVE TO GO UP 2 UNITS AND RIGHT 3 UNITS.
SO IF WE MOVE UP 2 UNITS THAT MEANS THE CHANGE IN Y
OR THE RISE WOULD BE +2
AND IF WE MOVE RIGHT 3 UNITS
THAT MEANS THE RUN OR THE CHANGE IN X WOULD BE 3.
THEREFORE THE SLOPE OF THIS LINE IS EQUAL TO 2/3.
AND THEN NOTICE HOW THIS LINE INTERSECTS THE Y AXIS AT +1
THEREFORE THE Y INTERCEPT IS EQUAL TO 1,
WHICH MEANS B = 1.
AND THIS IS ALL WE NEED TO DETERMINE
THE EQUATION OF THE LINE IN SLOPE INTERCEPT FORM.
OUR LINEAR EQUATION IS Y = 2/3X + 1.
NOW, I SHOULD MENTION THAT SINCE WE DID LIST THE COORDINATES
OF THESE 2 POINTS
WE COULD'VE USED THE FORMULA M = Y SUB 2 - Y SUB 1
DIVIDED BY X SUB 2 - X SUB 1
TO FIND THE SLOPE OF THIS LINE,
BUT I THINK JUST ANALYZING THE GRAPH IS A LOT FASTER.
AND IF YOU WANT YOU CAN USE THIS TO VERIFY
THE SLOPE WOULD BE 2/3.
I HOPE THIS WAS HELPFUL.