Question 92938
What is perpendicular to the graph of:
{{{3x-4y = 0}}}
You'll recall that if lines are perpendicular, then their slopes are the negative reciprocal of each other.  So putting your equation into the slope-intercept form (y = mx+b) where we can readily identify the slope, m:
{{{y = (3/4)x}}} ...and you can see that the slope, {{{m = 3/4}}} and you'll also notice that the y-intercept, b, is zero (This line passes through the origin)
Now that you have you slope, the slope of any line that is perpendicular to this one will be the negative reciprocal of 3/4 or -4/3, so you can write:
{{{y = (-4/3)x + b}}}
Notice that this equation is for a whole set of lines having the same slope, not just one line, and without additional information, such as the y-intercept, you really cannot identify a specific line, can you?
So the given answer {{{y = (-4/3)x + 12}}} certainly will be a correct answer, but so will your answer {{{y = (-4/3)x+0}}}(Green line)
The graph below should illustrate this quite clearly:(The graph of the given equation is in red)
{{{graph(600,400,-5,5,-4,4,(3/4)x,(-4/3)x,(-4/3)x+4,(-4/3)x+6)}}}