Question

Find the equation of the line perpendicular to y = -2x + 6 that goes through (2, 10).

Answer 1

If the line is perpendicular, then its slope is the reciprocal of the given line's slope. This new line's slope is 1/2. We plug it into slope-intercept form

y = 1/2x + b

Now plug in the given point of (2, 10) and solve for b.

10 = 1/2(2) + b
10 = 1 + b
9 = b

So your equation is y = 1/2x + 9