The given line has a slope of -1/3. Since we want a line perpendicular to this one, we need a slope that is the negative reciprocal of -1/3, which is 3.
So the slope of the line we want is 3, and it passes through the point (1, -10). We can use the point-slope form of a linear equation to find
the equation of the line:y - y1 = m(x - x1)where m
is the slope and (x1, y1) is the point.Plugging in
the values we have, we get:y - (-10) = 3(x -
1) Simplifying this equation, we get:y + 10 = 3x -
3Subtracting 10 from both sides, we get the final
equation:y = 3x - 13Therefore, the equation of
the line that passes through the point (1, -10)
and is perpendicular to y=-1/3x+5 is y = 3x - 13.