Question

In a xy plane, the equation of a line is `x+3y=12`. What is an equation of a line that is perpendicular to it?

Answer 1

`y=3x+c` (for all `c in RR`)
For example, `y=3x+4`

Explanation:

The equation of a straight line in slope (`m`) and intercept (`c`) form is:

`y = mx+c`

In this example we are given the equation: `x+3y=12`

Rearranging terms:
`3y=-x+12`

`y=-1/3x+4`

Hence: `m=-1/3` and `c=4`

For two straight lines to be perpendicular to eachother their slopes
(`m_1 and m_2`) must satisfy the relationship: `m_1xxm_2 =-1`

Hence the straight lines perpendicular to the line with a slope of `-1/3` will have slopes of `-1/(-1/3) = 3`

`:.` The straight lines perpendicular to the given line will have equations:

`y=3x+c` (for all `c in RR`)

For example, the line perpendicular to the given line with the same intercept is `y=3x+4`