Question

How do you find a standard form equation for the line with (6, -1) and is perpendicular to the line whose equation is 5x + 9y - 61 = 0?

Answer 1

`y=9/5x-59/5`

Explanation:

First, convert `5x+9y-61=0` into `y=mx+b`

`5x+9y-61=0`

Therefore, `y=-5/9x+61/9`

The perpendicular line to `y=-5/9x+61/9` will have a slope `m=9/5`, because the product of the perpendicular line's slope and the original line's slope (`m_1m_2`) will equal `-1`.

`y_2=9/5x+c` where `c` is the y-intercept

We know that it passes through `(6,-1)`. Plug that in to `y_2`.

`-1=54/5+c`

`c=-59/5`

Therefore, the equation of the line that passes through `(6,-1)` and is perpendicular to `5x+9y-61=0` is

`y=9/5x-59/5`