Question 78316
X-2Y=8
2Y=-X+8
Y=-X/2+8/2
Y=-X/2+4 THIS IS THE EQUATION IN LINE FORM WHERE -1/2 IS THE SLOPE (m) & 4 IS THE Y INTERCEPT(b) OR THE POINT (0,4).
THE LINE PERPENDICULAR TO THIS LINE WILL HAVE A SLOPE OF THE NEGATIVE RECIPRICAL OF THIS SLOPE THUS THE NEW SLOPE IS 2.
NOW WE USE THIS SLOPE (m) AND THE X&Y POINTS GIVEN & SOLVE FOR THE Y INTERCEPT.
-6=2*1+b
-6=2+b
b=-6-2
b=-8 WHICH IS THE Y INTERCEPT FOR THE PERPENDICULAR LINE WITH THE EQUATION OF
Y=2X-8
NOW WE'LL PLOT THE ORIGINAL LINE (RED) AND TRHE PERPENDICULAR LINE (GREEN).
{{{ graph( 300, 300, -10, 10, -10, 10, y = -x/2 +4, y = 2x -8) }}} (graph 300x300 pixels, x from -10 to 10, y from -10 to 10, of TWO functions y = -x/2 +4 and y = 2x -8).