What is the equation of the line perpendicular to #y=6x # that passes through # (6,-1) #?
Different way of saying the same thing:
Compare to the standard equation form of
Looking at the question we see that the gradient is 6.
This means that for 1 along on the x-axis the line has gone up 6 on the y-axis.
So the straight line perpendicular to that given has the equation
This line passes through the point
So by substitution
so the equation of the perpendicular line is:
When lines are perpendicular, one slope is the negative reciprocal of the other.
The slope perpendicular to this is
We now have the slope and the point
There is really nifty formula which applies in a case like this. We have the slope and one point and need to find the equation of the line.
Substitute the values given.