I was solving a problem. In
It r have been given that two lines are perpendicular to each other
The equation of one line
2x-3y+4=0
Now i have to find the equation of another line
We can find it by finding the slope of the abovementioned line( the other line)
But we are prohibited to do so
I have to find the equation of other line
So
Equation of line perpendicular to
ax+by+c=0
Is
bx-ay+c=0
Now I am confused whether we have to take the negative sign which is in front of b (is -3 here) in perpendicular form
And what Is the equation
ax+by+c=0 ----> bx-ay+c=0
What that says is :
interchange the coefficients of the x and y terms
then change the sign of the y term to its opposite.
Remember, it is considered to be "good form" to have the x term at the front as a positive term.
e.g.
5x + 7y + 9 = 0 , a perpendicular line would be
7x - 5y + C = 0
yours:
2x-3y + 4 = 0 ----> 3x + 2y + 4 = 0
I kept the constant at 4, it could have been anything.
The constant could be anything else and the new line would still be perpendicular, since the constant has no effect on the slope of a line.
Ahh interchange of coefficients of x and y and sign change of y
Now I get it
To find the equation of the line perpendicular to the given line (2x-3y+4=0), we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other.
The given line is in the form ax + by + c = 0, where a = 2, b = -3, and c = 4.
Now, let's use the formula for the equation of a line perpendicular to ax + by + c = 0:
The equation of a line perpendicular to ax + by + c = 0 is bx - ay + d = 0, where d is a constant.
In your case, since a = 2 and b = -3, the equation of the perpendicular line will be -3x - 2y + d = 0.
To determine the value of d, we can substitute the coordinates of a point lying on the line. For simplicity, let's use the point (0, 0).
Plugging in these values into the equation -3x - 2y + d = 0, we get:
-3(0) - 2(0) + d = 0,
0 + 0 + d = 0,
d = 0.
Therefore, the equation of the line perpendicular to 2x - 3y + 4 = 0 is -3x - 2y = 0.
Note: The negative sign in front of "b" (-3) in the perpendicular form is taken into account. No need to change it.