SOLUTION: Could you please help me answer this question? Find the equation for the line that passes through the point (4,-2), and that is perpendicular to the line with the equation 3/4x-3y=

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Question 420079: Could you please help me answer this question? Find the equation for the line that passes through the point (4,-2), and that is perpendicular to the line with the equation 3/4x-3y=-3. I have tried but seem to get stuck when it comes to fractions and solving for y. Any help is much appreciated! Thank you.
Found 2 solutions by ankor@dixie-net.com, mananth:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Find the equation for the line that passes through the point (4,-2), and that is perpendicular to the line with the equation 3/4x-3y=-3.
:
Find the slope of the given equation, put it in the slope/intercept form; y= mx+b
x - 3y = -3
-3y = x - 3
:
y has to be positive, multiply by -1
3y = x + 3
divide eq by 3
y = x + 1
Reduce fraction
y = x + 1
:
the slope of the given equation: m1 =
the slope relationship of perpendicular lines: m1*m2 = -1
Find m2
*m2 = -1
multiply both sides by 4
m2 = -4 is the slope of line perpendicular to the given equation
:
use the point/slope form to find the perpendicular line: y - y1 = m(x - x1)
we have: x1 = 4, y1 = -2, m = -4
y - (-2) = -4(x - 4)
y + 2 = -4x + 16
y = -4x + 16 - 2
y = -4x + 14, is the equation of the perpendicular line

Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
� x - 3 y = 3
Find the slope of this line
3 y = � x -3
Divide by 3
y = 0.25 x -1
Slope = 0.25

The slope of a line perpendicular to the given line will be the negative reciprocal
m1*m2=-1
The slope of the required line will be -4

m=-4 ,point ( 4 , -2 )
Find b by plugging the values of m & the point
-2 = -16 + b
b= 14

The required equation is y = -4 x + 14