How do you write the standard form of the equation of the line that is perpendicular to y=-4/3x-7 and contains (-5,-7)?

1 Answer
R. Nguyen
Jun 27, 2018

The standard form equation is 3x - 4y = 133x−4y=13.

Explanation:

The slope of our line is color(red)(-\frac{4}{3})−43. The slope of any perpendicular line is given by the negative reciprocal.

m' = -\frac{1}{m}

m' = \frac{1}{color(red)(-\frac{4}{3})}

m' = \frac{3}{4}

The second condition is that the line contains (color(blue)(-5), color(green)(-7)).

y = 3/4x + b

Substitute color(blue)(x = -5), color(green)(y = -7).

color(green)(-7) = 3/4(color(blue)(-5)) + b

color(green)(-7) = -15/4 + b

-13/4 = b

So in slope-intercept form, the equation of our line is

y = 3/4x - 13/4

but the question requires it in standard form. This means that it should be in the form

Ax + By = C

where A, B, and C are all integers and A is positive. In our equation, we will multiply by the lowest common denominator to eliminate the denominator.

4y = 3x - 13

<=> 3x - 13 = 4y

<=> 3x - 4y = 13

Related questions
See all questions in Equations of Perpendicular Lines
Impact of this question
3431 views around the world
You can reuse this answer
Creative Commons License