Answer
a) $x = -9$
b) $y=1/2x+13/2$
c) (-7/5, 29/5)
Work Step by Step
a)
$2x + y = 3$
$2x + y-2x = 3-2x$
$y = -2x + 3$
$m= -2$
slope of perpendicular line would be $1/2$
$ 1/2 = rise/run$
$1/2 = (6-2)/(-1-x)$
$1/2*4/4 = 4/(-1-x)$
$4/8 = 4/(-1-x)$
$8 =-1-x$
$8+1 = -1-x+1$
$9 = -x$
$9*-1 = -x*-1$
$-9=x$
b)
$y=mx+b$
$6 = m*-1+b$
$6 = 1/2 *-1 + b$
$6 = -1/2+b$
$6+1/2 = -1/2+b+1/2$
$13/2 = b$
$y=1/2x+13/2$
c)
$y=1/2x+13/2$
$y=-2x+3$
$1/2x+13/2 = -2x+3$
$2*(1/2x+13/2 = -2x+3)$
$x+13 = -4x+6$
$x+13+4x-13 = -4x+6+4x-13$
$5x = -7$
$5x/5 = -7/5$
$x = -7/5$
$y = -2x+3$
$y = -2*(-7/5)+3$
$y = 14/5 + 3$
$y= 29/5$
