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 $-\frac{1}{10}$

Finally, we want a line passing through (1,1) with slope $-\frac{1}{10}$:

$y-1 = -\dfrac{1}{10}(x-1) \iff y = -\dfrac{x}{10} + \dfrac{1}{10}+1 = -\dfrac{x}{10} + \dfrac{11}{10}$