Write the equation of the family of line that are perpendicular to 4x+3y-1=0

Aidyn Meza

Aidyn Meza

Answered question

2022-09-20

Write the equation of the family of line that are perpendicular to 4x+3y-1=0

Answer & Explanation

Zackary Galloway

Zackary Galloway

Beginner2022-09-21Added 17 answers

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

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