Question

Find the equation of a line that is perpendicular line to y = 10x - 45 and goes through (1, 1).

Answer 1

The line
`y = 10x - 45` is already written in the
`y = mx+q` form. This means that
`m` is the slope. If two lines are perpendicular, their slopes are the anti-inverse of each other, i.e. their product is -1.

So, our perpendicular line has a slope of
`-(1)/(10)`

Finally, we want a line passing through (1,1) with slope
`-(1)/(10)`:

`y-1 = -(1)/(10)(x-1) \iff y = -(x)/(10) + (1)/(10)+1 = -(x)/(10) + (11)/(10)`