Question

How do you write an equation of the line perpendicular to the line x - 5y = -10 and passing through the point (2,5)?

Answer 1

I found: `y=-5x+15`

Explanation:

I would use the relationship:
`y-y_0=m(x-x_0)`
Where `m` is the slope and `x_0,y_0` are the coordinates of your point.
The slope `m` of the perpendicular is given as: `m=-1/m_1` where `m_1` is the slope of your given line:
Your line can be written (isolating `y`):
`y=x/5+2` which has slope `m_1=1/5` (the coefficient of `x`).
So, the slope of the perpendicular will be:
`m=-5`
Finally you get:
`y-5=-5(x-2)`
`y=-5x+10+5`
`y=-5x+15`