Question

What is the equation of the line perpendicular to `y=-7/9x` that passes through `(5,1)`?

Answer 1

9x−7y=38

Explanation:

Product of slope of two perpendicular lines is always `-1`. As the equation is in slope-intercept form, its slope is `-7/9` and hence slope of perpendicular line will be `9/7`. Hence equation will be

`y=(9/7)*x+c`

Putting `x=5` and `y=1`, this becomes

`1=(9/7)*5+c` or `c=1-(45/7)`

i.e. `c=-38/7`

Hence equation is `y=(9/7)*x-38/7` which can be simplified to

`9x-7y=38`