Question 129653
FIRST YOU MUST CHANGE THE FORMULA TO A LINE FORMULA OF THE FORM Y=mX+b WHERE m=SLOPE & b=Y INTERCEPT.
7X-8Y=-2
-8Y=-7X-2
Y=-7X/-8-2/-8
Y=7X/8+1/4 NOW YOU HAVE A SLOPE=7/8 & A Y INTERCEPT=1/4 (RED LINE)
FOR A LINE TO BE PERPENDICULAR TO THIS LINE IT WILL HAVE A SLOPE = THE NEGATIVE RECIPRICAL OF THIS SLOPE. THUS THE SLOPE=-8/7.
BECAUSE THIS PERPENDICULAR LINE PASSES THROUGH (6,3) YOU NOW NEED TO REPLACE THE X & Y VALUES IN THE LINE EQUATION WITH THESE VALUES.
3=-8/7*6+b
3=-56/7+B
b=3+56/7
b=(21+56)/7
b=77/7
b=11 ANSWER FOR THE Y INTERCEPT.
THUS THE EQUATION FOR THIS PERPENDICULAR LINE IS:
Y=-8X/7+11 (GREEN LINE)
{{{ graph( 300, 200, -10, 10, -10, 10, 7x/8 +1/4, -8x/7 +11) }}} (graph 300x200 pixels, x from -10 to 10, y from -10 to 10, of TWO functions 7x/8 +1/4 and -8x/7 +11).