Find the equation of the line in slope-intercept form that is perpendicular to the line -4x - 3y = 9 and passes through (12, -7)

Payton Rasmussen

Payton Rasmussen

Answered question

2022-09-29

Find the equation of the line in slope-intercept form that is perpendicular to the line -4x - 3y = 9 and passes through (12, -7)

Answer & Explanation

Aniyah Liu

Aniyah Liu

Beginner2022-09-30Added 7 answers

- 4 x - 3 y = 9
can be re-written in slope intercept form as:
y = - 4 3 x - 3
and therefore has a slope of ( - 4 3 )

Lines which are perpendicular to each other have slopes that are the negative reciprocal of one another.

Therefore any line perpendicular to −4x−3y=9 has a slope of
m = 3 4

Since the desired line has a slope of 3 4 and passes through (12,−7) we can write it's equation in slope-point form as:
( y - ( - 7 ) ) = 3 4 ( x - 12 )

Simplifying:
y + 7 = 3 4 x - 9
or
y = 3 4 x - 16 XXXX which is slope-intercept form.

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