Question 54033
P(2,0);L(x+2y=3)
First put L in slope intercept form:{{{highlight(y=mx+b)}}}; m=slope; (0,b)=y-intercept
{{{x+2y=3}}}
{{{-x+x+2y=-x+3}}}
{{{2y=-x+3}}}
{{{2y/2=-x/2+3/2}}}
{{{y=(-1/2)x+3/2}}}
L has a slope of -1/2.
(a)Parallel lines have the same slopes, so the new line has a slope of -1/2 also.P(2,0)=(x1,y1)
Use the point slope formula {{{highlight(y-y1=m(x-x1))}}} to find the equation of the line:
{{{y-0=-1/2(x-2)}}}
{{{highlight(y=(-1/2)x+1)}}}
(b) Perpendicular lines have slopes that are negative reciprocals of each other. So flip -1/2 over and change the sign and your new line will have a slope m=2/1 or m=2.  P(2,0) Use the point slope formula to find the equation of the line again.
{{{y-0=2(x-2)}}}
{{{highlight(y=2x-4)}}}
Happy Calculating!!!