Find the equation of lines through origin ,perpendicular to the lines

Answer 1

The equation of a line that passes through the origin can be expressed in the form y = mx, where m is the slope of the line.

To find a line perpendicular to this line, we need to find the negative reciprocal of the slope of the original line. Let's call this new slope m'.

For two lines to be perpendicular, the product of their slopes must be -1. Therefore, m * m' = -1.

Now we can substitute the slope of the original line, m, into the equation:

m * m' = -1

This equation allows us to solve for m'.

For example, let's say the slope of the original line is 2. We can substitute this into the equation and solve for m':

2 * m' = -1

m' = -1/2

So the slope of the line perpendicular to y = 2x is -1/2.

Now we can write the equation of the line perpendicular to y = 2x that passes through the origin:

y = -1/2x