What’s the point slope equation of the line that is perpendicular to y-8=3(x-10) and passes through (-2,7)?

First off, let's take a peek at y-8=3(x-10), which is already in point-slope form



so, it has a slope of 3, so a line perpendicular to that one, will have a negative reciprocal slope to that,



so we're really looking for the equation of a line whose slope is -1/3 and runs through -2,7.