Find an equation for the line passing through the point (2, 3) and perpendicular to the line y=3x−16

Perpendicular lines have the opposite inverse slope of the other line. using y = mx + b, where m is the slope, we see.this line has a slope of 3. The opposite inverse of 3 is -1/3. So we know slope of perpendicular line is - 1/3.

now we can use y - y1 = m (x - x1) where m is the slope and (x1,y1) is the given point (2,3).
y - 3 = - 1/3 (x - 2)
y = - 1/3x - 2/3 + 3
y = - 1/3 + 7/3

What exactly is your question?