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LET'S TALK ABOUT HOW TO WRITE EQUATIONS OF SPECIAL LINES
NAMELY VERTICAL LINES AND HORIZONTAL LINES.
FIRST, LET'S DO A VERTICAL LINE.
A VERTICAL LINE HAS AN EQUATION OF THE FORM X = H,
WHERE H IS A CONSTANT.
SOME CHARACTERISTICS OF A VERTICAL LINE
ARE A VERTICAL LINE IS PARALLEL TO THE Y-AXIS.
SO HERE, I HAVE A LITTLE EXAMPLE OF A VERTICAL LINE X = H
AND NOTICE THAT IT IS PARALLEL TO THE Y-AXIS.
ANOTHER CHARACTERISTIC THAT IT'S PERPENDICULAR TO THE X-AXIS,
SO NOTICE THAT THIS VERTICAL LINE X = H
IS PERPENDICULAR TO THE X-AXIS.
WE CAN ALSO SAY THAT A VERTICAL LINE HAS NO SLOPE
OR THAT IT HAS UNDEFINED SLOPE.
SO LET'S LOOK AT THESE PROBLEMS THAT I HAVE OVER HERE,
AND LET'S TRY TO WRITE THE EQUATIONS OF THESE LINES.
FIRST ONE SAYS I HAVE A VERTICAL LINE
THROUGH (-5,5),
SO LET'S LOOK AT WHERE THIS IS APPROXIMATELY--
SO (-5,5), LET'S SAY, IS SOMEWHERE HERE.
I WANT TO DRAW A VERTICAL LINE THROUGH THAT POINT
SO NOTICE THAT THIS IS A VERTICAL LINE
AND THE X-COORDINATE OR THE X-INTERCEPT IS -5,
SO THE EQUATION OF THIS LINE IS X = -5.
THE NEXT PROBLEM THAT I HAVE IS I HAVE A LINE
PARALLEL TO THE Y-AXIS AND CONTAINS (1,3).
SO (1,3), LET'S SAY, IS SOMEWHERE HERE, OKAY,
AND THE LINE THAT I WANT IS PARALLEL TO THE Y-AXIS.
SO AGAIN, NOTICE I DRAW A VERTICAL LINE RIGHT THERE
SO IT CROSSES THE X-AXIS AT 1,
SO THE EQUATION OF THIS VERTICAL LINE IS X = 1.
FOR THE THIRD PROBLEM,
I HAVE A LINE THAT GOES THROUGH THIS POINT (1/2,-3/4).
(1/2,-3/4), LET'S SAY, IS SOMEWHERE HERE
AND I WANT IT TO BE PERPENDICULAR
TO THE X-AXIS.
THERE IS THE X-AXIS.
I DRAW A LINE PERPENDICULAR TO IT.
YOU SEE THAT I GET A VERTICAL LINE
THAT GOES THROUGH THE X-INTERCEPT 1/2,
SO THIS LINE WILL HAVE EQUATION X = 1/2.
FINALLY, I HAVE A LINE THAT HAS NO SLOPE
AND PASSES THROUGH THE POINT (-4,-2).
SO (-4,-2), LET'S SAY, IS SOMEWHERE HERE
AND I KNOW IT HAS NO SLOPE,
SO I KNOW THAT A LINE THAT HAS NO SLOPE
IS A VERTICAL LINE,
AND THIS LINE WILL HAVE EQUATION X = -4.
SO IF YOU NOTICE,
TO GET AN EQUATION OF A VERTICAL LINE
GOING THROUGH A POINT,
ALL WE DO IS GRAB THE FIRST COORDINATE
OF THE POINT.
AND THAT'S HOW YOU WRITE AN EQUATION OF A VERTICAL LINE.