Answer
4y−3x=19
Solution
The the products of the gradients of perpendicular lines is −1 , that is, mm′=−1 where m is the gradient of one line and m′ is the gradient of a line perpendicular to the first line.
The general form of a straight line equation is y=mx+c . Reducing 3y+4x=1 to standard form gives:
3y+4x=1
=>3y=−4x+1
=>33y=3−4x+31
=>y=−34x+31
Now, the gradient is −34
Since mm′=−1
=>−34m′=−1
=>−4m′=−1×3
=>m′=−4−3
=43
Thus, the perpendicular line has gradient 43
The equation of the perpendicular line through A is given by:
y−y1=m′(x−x1)
=>y−4=43(x−(−1))
=>y=43(x+1)+4
=>4y=3(x+1)+16
=>4y=3x+3+16
=>4y−3x=19
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