- WELCOME TO AN ANIMATION OF A LINE IN THE FORM Y = MX + B.
THE GOAL OF THE VIDEO IS TO ILLUSTRATE
HOW CHANGING THE VALUE OF M AND B
CHANGE THE GRAPH OF A LINE IN SLOPED INTERCEPT FORM.
AND JUST TO REFRESH YOUR MEMORY,
IF A LINE IS IN THE FORM Y = MX + B
M = THE SLOPE OF THE LINE AND B = THE Y INTERCEPT OF THE LINE.
SO HERE WE SEE A LINE GRAPHED ON THE COORDINATE PLANE
AND HERE WE SEE THE EQUATION OF THE LINE.
SO THE CURRENT LINE HAS SLOPE 0.321.
FIRST THING I'M GOING TO DO IS CHANGE THE VALUE OF THE SLOPE
AND LEAVE THE Y INTERCEPT THE SAME.
AND I'D JUST LIKE YOU TO WATCH HOW THE LINE CHANGES
AS WE CHANGE THE SLOPE.
OKAY I'M GOING TO PAUSE THE LINE HERE.
NOW, WHAT I WANT YOU TO NOTICE IS THE SLOPE IS POSITIVE.
IT'S 0.481.
AND AS I INCREASE THE SLOPE
THE LINE BECOMES MORE SLANTED OR MORE STEEP.
ANOTHER THING I'D LIKE YOU TO NOTICE
IS IF THE SLOPE IS POSITIVE,
THE LINE DOES GO UP FROM LEFT TO RIGHT.
SO MOVING FROM LEFT TO RIGHT THE LINE IS GOING UP.
AND AGAIN AS WE INCREASE THE SLOPE
THE LINE GOES UP EVEN FASTER FROM LEFT TO RIGHT.
LET'S PAUSE THE LINE HERE FOR A MOMENT.
HERE WE CAN SEE OUR SLOPE IS APPROXIMATELY 3 OR 3/1.
REMEMBER WHAT THAT MEANS IS THAT WE PICK A POINT ON THE LINE.
TO FIND ANOTHER POINT ON THE LINE
WE'D HAVE TO GO UP APPROXIMATELY 3 UNITS AND OVER 1.
SO IF I CHANGE THE SLOPE TO LET'S SAY 6 OR ROUGHLY 6,
THAT MEANS I'D HAVE TO GO UP 6 AND RIGHT 1
TO FIND ANOTHER POINT ON THE LINE
WHICH MAKES THE LINE MUCH MORE STEEP
THAN WHEN THE SLOPE IS EQUAL TO 3.
SO IF I INCREASE IT TO 9
PICKING A POINT ON THE LINE
WE'D HAVE TO GO UP 9 UNITS AND RIGHT ONE.
SO AS THE SLOPE INCREASES THE LINE BECOMES MORE STEEP
FROM LEFT TO RIGHT.
NOW, AS WE DECREASE THE SLOPE
THE LINE WILL BECOME LESS SLANTED.
AND WHAT I WANT YOU TO DO IS WATCH ONCE IT TURNS NEGATIVE.
ONCE THE SLOPE TURNS NEGATIVE
YOU'LL NOTICE THE LINE IS SLANTED DOWN FROM LEFT TO RIGHT.
SO NEGATIVE SLOPES WILL SLANT DOWN FROM LEFT TO RIGHT
AND AS WE DECREASE THE SLOPE FURTHER
YOU CAN SEE IT BECOMES SLANTED DOWN EVEN MORE.
SO IF I PAUSE HERE AND LOOK AT THE SLOPE OF -3
IF I PICK A POINT ON THE LINE I'D HAVE TO GO DOWN 3 UNITS
AND RIGHT 1 TO FIND ANOTHER POINT ON THAT LINE.
IF I CHANGE THE SLOPE TO -6 USING THE SAME IDEA,
I'D HAVE TO PICK A POINT AND NOW GO DOWN 6 UNITS
AND RIGHT 1 TO FIND ANOTHER POINT ON THE LINE.
SO IT BECOMES EVEN STEEPER DOWNHILL FROM LEFT TO RIGHT.
THE LAST THING I WANT TO POINT OUT, NOTICE THAT THE SLOPE IS 0.
WE HAVE A HORIZONTAL LINE
AND THE X TERM DISAPPEARS FROM OUR EQUATION.
WE HAVE Y EQUAL TO A CONSTANT.
OKAY LET'S GO AND TAKE A LOOK AT THE EFFECT
OF CHANGING THE VALUE OF B OR THE Y INTERCEPT.
NOTICE HOW CHANGING THE VALUE OF B
DOES NOT CHANGE HOW THE LINE IS SLANTED,
IT JUST SHIFTS A LINE UP OR DOWN.
SO IF WE PAUSE HERE FOR A MOMENT
NOTICE THAT THE Y INTERCEPT IS APPROXIMATELY 3
AND THAT IS EXACTLY WHERE THE LINE CROSSES THE Y AXIS.
IF I PAUSE AT APPROXIMATELY B = 1
WE HAVE A Y INTERCEPT OF 1.
IF WE PAUSE HERE THE VALUE OF B WOULD BE APPROXIMATELY -2
AND WE HAVE A Y INTERCEPT OF APPROXIMATELY -2 AND SO ON.
SO THE VALUE OF B WILL GIVE US THE Y INTERCEPT OF THE LINE
AND IT DOES NOT AFFECT HOW THE LINE IS SLANTED,
THAT'S CONTROLLED BY THE SLOPE.
I HOPE YOU FOUND THIS ANIMATION HELPFUL.