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Find an equation of the line, which is perpendicular to the line

3x −4y = 5 and passes through point P (1, −1).

User Yazaki
by
8.1k points

1 Answer

1 vote

Answer:

4x + 3y = 1

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given the line

3x - 4y = 5 ( subtract 3x from both sides )

- 4y = - 3x + 5 ( divide through by - 4 )

y =
(3)/(4) x -
(5)/(4) ← in slope- intercept form

with slope m =
(3)/(4)

given a line with slope m then the slope of a line perpendicular to it is


m_(perpendicular) = -
(1)/(m) = -
(1)/((3)/(4) ) = -
(4)/(3) , then

y = -
(4)/(3) x + c ← is the partial equation of the perpendicular line

to find c substitute P (1, - 1 ) into the partial equation

- 1 = -
(4)/(3) (1) + c = -
(4)/(3) + c ( add
(4)/(3) to both sides )


(1)/(3) = c

y = -
(4)/(3) x +
(1)/(3) ← in slope- intercept form

multiply through by 3 to clear the fractions

3y = - 4x + 1 ( add 4x to both sides )

4x + 3y = 1 ← equation of perpendicular line in standard form

User Ivan Denysov
by
8.6k points