How do you write an equation of a line, given $(4,5)$ that is perpendicular to the line $3x-4y=7$ ?

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Answer 1 · 2017-06-30T19:30:05

$4x +3y=31$

Rearrange the original equation into form: $y=mx+c$

$(y=3/4x-7/4).$

The perpendicular gradient is the negative reciprocal of $3/4$
(just change the sign and flip the fraction upside down)
which is $-4/3$ .

Now use $y-y_1=m(x-x_1) ,$ substituting the $4 and 5$ .

$y -5 = -4/3(x-4)$

Rearrange the resulting equation (usually asked for in integer form)

$y -5 = -4/3x+16/3" "xx3$

$3y-15 = -4x +16$

$4x +3y = 31$

How do you write an equation of a line, given (4,5)(4,5) that is perpendicular to the line 3x-4y=73x-4y=7?