Question 844453
(i)
If parallel, then the coefficients on x and y are unchanged; but the constant term will be different.

{{{3x-2y+p=0}}} is a parallel line for any {{{p<>4}}}.
Solving for p and then using (3,4),
{{{p=2y-3x}}}
{{{p=2*4-3*3}}}
{{{p=-1}}}
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The parallel line is {{{highlight(3x-2y-1=0)}}}.


(ii)
Sufficient understanding of the standard form of the equation, know that the slope is {{{3/2}}}, and then the slope of a line perpendicular to the given line must be {{{-(2/3)}}}.  The equation we want is {{{2x+3y+r=0}}} and we want to use the given point to solve for r. (One should examine standard form and compare to slope-intercept form to learn how you can use standard form).
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First solve symbolically for r.
{{{r=-2x-3y}}}.
Substitute the point that it should contain.
{{{r=-2*3-3*4}}}
{{{r=-6-12}}}
{{{r=-18}}}
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Now knowing r, the equation containing (3,4) and perpendicular to 3x-2y+4=0 is {{{highlight(2x+3y-18=0)}}}.