How do you write the equation of the family of line that are perpendicular to 4x+3y-1=0?

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Answer 1 · 2018-03-24T16:26:22

#y=-3/4x+b#

Rearrange #4x+3y-1=0# to be an explicit function of x:

#y=-4/3x-1/3#

If two lines are perpendicular, then the product of their gradients is #-1#

i.e.

If the gradients are #m_1# and #m_2#:

#m_1*m_2=-1#

#m_2=1/m_1#

Let # \ \ \ \ m_1=-4/3#

Then:

#m_2=1/(-4/3)=-3/4#

Any line of the form:

#y=-3/4x+b#

Will be perpendicular to #\ \ \ \ y=-4/3x-1/3#