Since the equation must be expressed in standard form, that is, Ax+By=C, we can find the perpendicular line by switching the coefficients of x and y and changing the operation sign.
But first let's rewrite the given equation in Ax+By=C form.
3x+4y-12=0
3x+4y=12
To find the perpendicular line, switch the coefficients of x and y and change the operation sign. By doing so we get:
4x-3y=C; where C is any constant but we are given the point (-6,7) so we can substitute these values for x and y to find C.
If we let (-6,7)->(x,y) then,
4(-6)-3(7)=C
-24-21=C
-45=C
So we found our constant. We can now substitute this value for C for the equation of the perpendicular line. In doing so, we get our final equation:
4x-3y=-45larr And this is the equation of the perpendicular line