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Question 92938: In the x,y plane, what is perpendicular to the graph of the linear equation 3x-4y=0
I've done this over and over but i can't figure it out. The answer is supposed to be y=-(4/3)x+12 but i keep getting y=(3/4)x+0. Thank you for your help!
Found 2 solutions by scott8148, Earlsdon:
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! perpendicular means that the slopes are negative reciprocals of each other
the original line has a slope of 3/4, so the perpendicular line has a slope of -4/3
3x-4y=0 ... -4y=-3x+0 ... y=(3/4)x+0 (y=mx+b)
can't tell where the 12 comes from ... judging from the question, the 12 could be any number - it is the slope that's important
Answer by Earlsdon(6294)  (Show Source):
You can put this solution on YOUR website! What is perpendicular to the graph of:
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:
 ...and you can see that the slope,  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:
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  certainly will be a correct answer, but so will your answer  (Green line)
The graph below should illustrate this quite clearly:(The graph of the given equation is in red)
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