Question 938111
the standard slope-intercept form for an equation of a line is 
{{{y = highlight_green(m)x + highlight(b)}}}  
where m is the slope and b the y-intercept
...
the line L, given by the equation 6x - 3y = 15  0r y = 2x - 5(Green),  m = 2

***Using point-slope form, {{{y - y[1] = highlight_green(m)(x - x[1])}}} P(2,8)
A. parallel  to L, m = 2/1
y - 8 = 2(x-2)
y = 2x + 4 (Blue)  0r 2x-y = -4
....
B. perpendicular to L, m = -1/2 (negative reciprocal of 2  {{{(2/1)(-1/2) = -1}}}
y - 8 = -1/2(x-2)
y = (-1/2)x + 9(Purple)  0r x + 2y = 18
{{{drawing(300,300,    -10,10,-10,10,   
 grid(1),
circle(2,8,0.4),
circle(0,-5,0.4),
graph( 300, 300, -10,10,-10,10,0, 2x - 5,2x+4, -.5x+9))}}}