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)passes through the

Algebra ->  Circles -> 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)passes through the      Log On


   

Question 872789: 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)passes through the origin
b) passes through the point (4,-6)
Can you please help me out? Thanks so much in advance:)
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
x-2y=4
and
4x-y=4
--
[ x-2y=4 ]
[ 8x-2y=8 ]

8x-2y-%28x-2y%29=4
7x=4
x=4%2F7
-
y=4x-4
y=4%284%2F7%29-4
y=16%2F7-28%2F7
y=-12%2F7
-
Intersection point, (4/7,-12/7).

The line formed by the found point and the origin:
In this situation, y intercept is zero.
y=mx, and we can use slope formula to easily find slope; or we can see the slope from the found point.
From the origin, that point is found on the slope -12%2F4=-3.
(a) Answer is highlight%28y=-3x%29.

(b) is not much harder. Just that the slope will be different, and y-intercept will not be zero but something else.