SOLUTION: 2 perpendicular lines intersect on the x axis. One of the lines is 2x-y +3=0 find the equation of the second line. Write your answer in general form

Algebra ->  Linear-equations -> SOLUTION: 2 perpendicular lines intersect on the x axis. One of the lines is 2x-y +3=0 find the equation of the second line. Write your answer in general form      Log On


   

Question 1079202: 2 perpendicular lines intersect on the x axis. One of the lines is 2x-y +3=0 find the equation of the second line. Write your answer in general form
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The given line is:
+2x+-+y++%2B+3+=+0+
+y+=+2x+%2B+3+
The slope is +m%5B1%5D+=+2+
Any line perpendicular to this line
will have slope +m%5B2%5D+=+-1%2F2+
-------------------------------
The lines intersect at ( x1, 0 )
For the given line:
+0+=+2%2Ax%5B1%5D+%2B+3+
+2x%5B1%5D+=+-3+
+x%5B1%5D+=+-3%2F2+
-----------------
The unknown line is:
+y+=+%28-1%2F2%29%2Ax+%2B+b+
Plug in the point ( -3/2, 0 )
+0+=+%28-1%2F2%29%2A%28-3%2F2%29+%2B+b+
+%28+3%2F4+%29+%2B+b+=+0+
+b+=+-3%2F4+
-------------------------
The unknown line is:
+y+=+%28-1%2F2%29%2Ax+-+3%2F4+
+4y+=+-2x+-+3+
+2x+%2B+4y+%2B+3+=+0+
-------------------------
Here's the plot of the 2 lines:
+graph%28+400%2C+400%2C+-6%2C+6%2C+-6%2C+6%2C+2x+%2B+3%2C+%28-1%2F2%29%2Ax+-+3%2F4+%29+

Answer by ikleyn(52824) About Me  (Show Source):
You can put this solution on YOUR website!
.
For the given line, the x-intercept is x = -1.5  (it makes y = 0).


So, we need to find the equation of the line perpendicular to the given line and passing through the point (-1.5,0).


The given line has the slope 2 (because the equation of the given line in the slope-form is y = 2x+3).


Hence, the slope of the perpendicular line is -0.5.


The straight line with the slope -0.5 through the point (-1.5,0) is

y - 0 = (-0.5)*(x-(-1.5)),   or

y = -0.5*(x+1.5).


It is the same as 

2y = -(x+1.5),   or

4y = - 2x - 3,   or

2x + 4y + 3 = 0,


on your choice.

Solved.     And plotted:



Plot y = 2x+3 (red) and y = -0.5*(x+1.5) (green)