You can put this solution on YOUR website! I'm assuming that this question meant to say that it is a line that passes through the point (6,-2) and is perpendicular to the line y = -2x+8.
We have a point and we are able to figure out the slope. So when we have a point and slope, we use the point-slope form.
The point-slope form is y-y1 = m(x-x1) where (x1,y1) is our point and m is our slope.
The point is easy. x1 =6, y1 = -2.
The slope is a little harder but they tell us that we are perpendicular to the line y = -2x+8. Perpendicular lines have slopes that are "opposite reciprocals". In other words, the slope of the line y = -2x + 8 has slope -2. So the "opposite reciprocal" of that is 1/2. [think we flipped the fraction and changed the sign].
So now it is a matter of just plugging in.
y - (-2) = 1/2(x-6)
y + 2 = 1/2(x-6)
y + 2 = 1/2x - 3
