What is the equation of the line, in slope-intercept form, that is perpendicular to the line with the equation y=6x−1 and passes through the point (−6,4)?
y=−6x+10
y=−1/6x−163
y=6x+40
y=−1/6x+3
y=6x+22

Perpendicular means has slope that multiplies to -1

y=6x-1
slope=6

6 times what=-1
what=-1/6

so

the equation of a line that passes through the point (x1,y1) and has a slope of m is
y-y1=m(x-x1)
given
point (-6,4) and slope is -1/6

y-4=-1/6(x-(-6))
y-4=-1/6(x+6)
expand
y-4=-1/6x-1
y=-1/6x+3

4th choice

The answer would be the second choice : )