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

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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)   (Show Source): You can put this solution on YOUR website!
The given line is:


The slope is
Any line perpendicular to this line
will have slope
-------------------------------
The lines intersect at ( x1, 0 )
For the given line:



-----------------
The unknown line is:

Plug in the point ( -3/2, 0 )



-------------------------
The unknown line is:



-------------------------
Here's the plot of the 2 lines:


Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.
For the given line, the x-intercept is x =   (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)



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