The equation for line j can be written as y=2x+8 Another line k is perpendicular to line j and passes through the point (6, -6). choose the equation for line k

The slope of a perpendicular line is its opposite reciprocal

So in this case, the perpendicular line for y=2x+8 is y=-1/2x+8

But we are looking for a different y-intercept since the equation has to pass through (6,-6), so we have -6=-1/2(6)+b and we can solve for b:

-6=-1/2(6)+b

-6=-3+b

-3=b

So the equation for line k is y=-1/2x-3

Hope this helped. Comment below if you'd like me to clarify anything.

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