Question

Which is the equation of a line perpendicular to 3x - 4y = 12.

Answer 1

Given the equation of a line

`3x-4y=12`

Any line perpendicular to the given line will have a slope equal to the inverse negative of the slope of the given line.

If you have, for example, two lines:

`\begin{gathered} y=mx+b \\ y=nx+c \end{gathered}`

And both lines are perpendicular, then the slope of the second line will be the inverse negative of the slope of the first line, and vice versa

`n=-(1)/(m)`
`m=-(1)/(n)`

So, first step is to write the given line is slope-intercept form:

`\begin{gathered} 3x-4y=12 \\ -4y=12-3x \\ -(4y)/(-4)=(12)/(-4)-(3x)/(-4) \\ y=-3+(3)/(4)x \\ y=(3)/(4)x-3 \end{gathered}`

The slope of the given line is

`m=(3)/(4)`

The slope of the line perpendicular to this one will be

`\begin{gathered} n=-(1)/(m) \\ n=-(4)/(3) \end{gathered}`

The line perpendicular to the given one will have a slope equal to -4/3