Question

Question #4ff0f

Answer 1

`y = -5/9*x+7/9` if you solve for `y`
`x=-9/5y+7/5` if you solve for `x`

Explanation:

It depends on what you want to solve for. I'll solve for `y`, which I'd guess is the most likely candidate:

Start with:
`(y-1)/(1/2-1)=(x+2/5)/(1/2+2/5)`

I'm going to simplify both denominators first:

`1/2-1=-1/2` while `1/2+2/5 = (5+4)/10=9/10`

so we have:
`(y-1)/(-1/2)=(x+2/5)/(9/10)`

I'll simplify the complex fractions:

`-2(y-1)=10/9(x+2/5)`

expand the right side:

`-2(y-1) = 10/9*x+20/45`

Simplify `20/45` to `4/9`

`-2(y-1) = 10/9*x+4/9`

divide both sides by `-2`:

`y-1 = -10/18*x-4/18`

Simplify fractions on the right side:

`y-1 = -5/9*x-2/9`

add 1 to both sides:

`y = -5/9*x+7/9`

If we wanted to solve for `x`, now is a good time:

Start with:
`y = -5/9*x+7/9`

subtract `7/9` from both sides:

`y-7/9=-5/9x`

multiply through by `-9`:

`-9y+7=5x`

divide through by 5:

`x=-9/5y+7/5`