Question

line through point (4,3) that is perpendicular to the line y=4x-2

Answer 1

What do you know about the slopes of perpendicular lines?

Answer 2

the line y=4x-2
the slope here is m=4
for perpendicular line its slope is m2=-1/m1
m2=-1/4
now use the point (4,3) and m=-1/4 to get the equation of the line using
y-y1=m(x-x1)