Question 1207841
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Determine whether each pair of lines is parallel, perpendicular, or neither.

(a) 3x + 4y = 12; 4x - 3y = -12

(b) y = 1; y = -1
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<pre>
(a)  Line 3x + 4y = 12  is the same as  y = {{{3 - (3/4)x}}}.

     From this form, you see that the slope of this line is {{{m[1]}}} = {{{-3/4}}}.


     Line 4x - 3y = -12  is the same as  y = {{{-4 + (4/3)x}}}.

     From this form, you see that the slope of this line is {{{m[2]}}} = {{{4/3}}}.


     The slopes  {{{m[1]}}}  and {{{m[2]}}}  are reciprocal: their product is -1.

     It means that the lines are perpendicular.    <U>ANSWER</U>




(b)  Line y = 1 is horizontal line parallel to x-axis.

     Line y = -1 is another/different horizontal line parallel to x-axis.

     Hence, lines y = 1  and  y = -1 are parallel.    <U>ANSWER</U>


      They both have the same slope of 0.
</pre>

Solved.