Question

How do you find the equation of the line that passes through ( -2 , 7 ) and is PERPENDICULAR to x + 5y = 7?

Answer 1

I found: `y=5x+17`

Explanation:

I would use the general form of the equation as:
`y-y_0=m(x-x_0)`
where:
`m=`slope
`x_0,y_0` are the coordinates of your point.
Now, to be perpendicular to your line `m` must be equal to `-1/(m')` where `m'` is the slope of your given line.
Your line can be written as:
`y=-1/5x+75` (isolating `y`);
with `m'=-1/5`
and so:
`m=5`
using this and your coordinates you have:
`y-7=5(x+2)`
`y=5x+10+7`
`color(red)(y=5x+17)`