Question 155784
First, lets graph {{{y=abs(-5x)}}}. Remember, we can break {{{abs(-5x)}}} into {{{-5x}}} and {{{-(-5x)=5x}}}



So first graph {{{y=-5x}}}



{{{graph(500,500,-10,10,-8,12,-5x)}}} Graph of {{{y=-5x}}}



Now graph {{{y=5x}}}



{{{graph(500,500,-10,10,-8,12,5x)}}} Graph of {{{y=5x}}}



Together, they look like this:




{{{graph(500,500,-10,10,-8,12,-5x,5x)}}} Graph of {{{y=-5x}}} (red) and graph of {{{y=5x}}} (green)


Now because the sign outside the absolute value is positive (ie there is no sign), this tells us to only draw the upper portion like this:




{{{graph(500,500,-10,10,-8,12,abs(-5x))}}} Graph of {{{y=abs(-5x)}}} 



Now let's graph {{{y=5*abs(x)}}}. To do this, first graph {{{abs(x)}}} (which is simply a "v" shaped graph):



{{{graph(500,500,-10,10,-8,12,abs(x))}}} Graph of {{{y=abs(x)}}} 



Now vertically stretch the graph by a factor of 5 to get the graph of {{{y=5*abs(x)}}}



{{{graph(500,500,-10,10,-8,12,5*abs(x))}}} Graph of {{{y=5*abs(x)}}} 



Notice that if you graph the two equations together you get




{{{graph(500,500,-10,10,-8,12,abs(-5x),5*abs(x))}}}  Graph of {{{y=abs(-5x)}}} (red) Graph of {{{y=5*abs(x)}}} (green)



So this means that the two graphs are identical (since one is right on top of the other)