Question 252784: Write an equation of the line through the point (a) parallel and (b)perpendicular to the given line:
(4,-5) l:-3x+5y=5
Answer by palanisamy(496)   (Show Source):
You can put this solution on YOUR website! The equation of the given line is -3x+5y = 5 ...(1)
The equation of a line parallel to this line is -3x+5y = k ...(2)
where k is a constant.
We are given that this line passes through the point(4,-5)
Put x=4 and y=-5 in (2)
We get, -3*4+5*(-5) = k
-12-25 = k
k = -37
Therefore,the equation of a line parallel to the given line through the point(4,-5)is -3x+5y = -37 or 3x-5y=37 ....(3)
Next, the equation of a line perpendicular to the given line is 5x+3y = c ..(4)
where c is a constant.
We are given that this line passes through the point(4,-5)
Put x=4 and y=-5 in (4)
We get, 5*4+3*(-5) = c
20-15 = c
c = 5
Therefore,the equation of a line perpedicular to the given line through the point(4,-5)is 5x+3y=5 ....(5)
|
|
|
