Question 314783
{{{3x=4y+5}}}
{{{4y=3x-5}}}
{{{y= (3/4)x-5/4}}}
Parallel lines have equal slopes.
{{{m1=m2=3/4}}}
Use the point-slope form of a line,
{{{ y-yp=m(x-xp)}}}
{{{y-(-3)=(3/4)(x-2)}}}
{{{highlight_green( y+3=(3/4)(x-2))}}}
Convert to slope-intercept form, {{{y=mx+b}}}
{{{y+3=(3/4)x-(3/2)}}}
{{{y+3=(3/4)x-(3/2)-(6/2)}}}
{{{highlight_green( y= (3/4)x-9/2 )}}}
{{{ drawing( 300, 300, -5, 5, -5, 5,grid(1),circle(2,-3,.2),graph( 300, 300, -5, 5, -5, 5, (3/4)x-9/2, (3/4)x-5/4 )
) }}}