Question 249105
Are the graph of the lines in the pair parallel?  Explain.

y=5x+6   ...and...   -18+3y=-54


Facts:  
1.  Two parallel lines share the same slope.
2.  To determine a slope, express the equations in this form: {{{y=mx+b}}}
3.  m = slope


{{{y=5x+6}}}  <--- already in y=mx+b form


{{{-18+3y=-54}}}
{{{3y=-54+18}}}
{{{3y=-36}}}
{{{y=-36/3}}}
{{{y=-12}}}  <--- there is no x value, thus we cannot express it in y=mx+b form


The answer is: they are not parallel because they do not share the same slope.


Here is how the graph of {{{y=5x+6}}} looks like:
{{{graph (300, 300, -7, 7, -7, 7, 5x+6)}}}


The slope of {{{y=-12}}} is zero, because it represents a horizontal line in the cartesian plane.
We know that a slope = rise/run... in this case there is no rise and the run goes to infinity (+ and - directions).  When zero is divided by any number, the result is zero... thus the slope is zero.
Here is how the graph of {{{y=-12}}} looks like:
{{{graph (300, 300, -7, 7, -18, 7, -12)}}}