Question

How do you write an equation in standard form given a line that passes through (-9,-3) and perpendicular to `y=-5/7*x-9`?

Answer 1

The line has equation `-7/5x+y=48/5`

Explanation:

we are looking for an equation of a line, that:

1. is perpendicular to `y=-5/7x-9`
2. passes through #(-9,-3)

ad. 1

If a line `y=a_1x+b_1` is perpendicular to `y=a_2x+b_2` then `a_1*a_2=-1` so we look for a number a for which `-5/7a=-1` which makes `a=7/5`

ad. 2

Now we have to find `b` for which the line passes through `(-9,-3)`. So we substitute `x=-9` abd `y=-3` in `y=7/5x+b`

`-3=7/5*(-9)+b`
`-3=-63/5+b`
`b=63/5-15/5`
`b=48/5`

So we get the equation `y=7/5x+48/5`.

Now to transfer it to th standard form we move terms containing `x` and `y` to the left and the free term to the right, sio we get:

`-7/5x+y=48/5`