SOLUTION: Write the equation of the line which passes through the point of intersection of the lines x-2y-4 = 0 and 4x-y-4 = 0 and satisfying the additional conditions a) parallel to the l

Question 872791: Write the equation of the line which passes through the point of intersection of the lines x-2y-4 = 0 and 4x-y-4 = 0 and satisfying the additional conditions
a) parallel to the line 16x -11y +3 =0
b) perpendicular to the line 9x + 22y - 8 =0
Can you please help me out? Thanks so much in advance:)
Found 2 solutions by mananth, josmiceli:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Write the equation of the line which passes through the point of intersection of the lines x-2y-4 = 0 and 4x-y-4 = 0 and satisfying the additional conditions
a) parallel to the line 16x -11y +3 =0
b) perpendicular to the line 9x + 22y - 8 =0

Solve x-2y-4 = 0 and 4x-y-4 = 0
to get (x,y)
1 x -2 y = 4 .............1

4 x -1 y = 4 .............2
Eliminate y
multiply (1)by 1
Multiply (2) by -2
1 x -2 y = 4
-8 x + 2 y = -8
Add the two equations
-7 x = -4
/ -7
x = 1
plug value of x in (1)
1 x -2 y = 4
1 -2 y = 4
-2 y = 4 -1
-2 y = 3
y = -2

(1,-2) is the point of intersection
16 x -11 y = -3
Find the slope of this line
make y the subject
-11 y = -16 x -3
Divide by -11
y = 1 4/9 x + 2/7
Compare this equation with y=mx+b
slope m = 1 4/9
The slope of a line parallel to the above line will be the same
The slope of the required line will be 1 4/9
m= 1 4/9 ,point ( 1 , -2 )
Find b by plugging the values of m & the point in
y=mx+b
-2 = 16/11 + b
b= -3.45
m= 13/9
Plug value of the slope and b in y = mx +b
The required equation is y = 13/9 x -38/11

for perpendicular take the negative reciprocal of the slope of given line 9x + 22y - 8 =0
and point is (1,-2)
frame the equation
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Find the (x,y) location of the intersection
of the lines:
(1)
(2)
--------------------------
Multiply (1) by and
subtract (1) from (2)
(2)
(1)
------------------------------

----------------------
Plug this back into (1) or (2)
(1)
(1)
(1)
(1)
The intersection is at ( 4/7, -12/7 )
--------------------------------------
(a) Find the slope of this line

The slope is
----------------------------
You can use the point-slope formula

Multiply both sides by

------------------------------------
That's it unless I made a mistake.
That's all I have time for

RELATED QUESTIONS
Write the equation of the line which passes through the point of intersection of the... (answered by josgarithmetic)
find the equation of circle passing through the points of intersection of the lines x +... (answered by MathLover1)
find the equation of circle passing through the points of intersection of the lines x... (answered by Alan3354)
Find the equation of the line that passes through (−3, 2) and the intersection of... (answered by Alan3354)
Hello. Please help me! Due tomorrow :( Find the equation of the line which passes... (answered by KMST)
Write down the general equation in terms of k of a line which passes through P, the point (answered by ikleyn)
Write an equation of the line which passes through these points (0, -4) and (0,... (answered by jim_thompson5910,Edwin McCravy)
Write the equation of the line which passes through (0, -4) and is parallel to the line... (answered by mananth)
Write the equation of the line which passes through (0, -4) and is parallel to the line... (answered by mananth)