Perpendicular lines have a slope that is the negative reciprocal of the original line equation. So, if our first line has the slope of m in the line equation y=mx+b, the perpendicular line would have a slope of -1/m.
Now, addressing the problem, we see that the line equation is y=6x-2. The slope would be 6. The perpendicular line would have a slope of -1/6.
Now, we rewrite the equation for the perpendicular line as y=-1/6x+b.
Next, we are given a point (6,-2). These are the coordinates for an x and a y such that (x,y). So, x=6 and y=-2.
This means, we can plug in our point into our perpendicular line equation to solve for b.
y=-1/6x+b
-2=-1/6(6)+b
-2=-1+b
-1=b
We now plug our value for b back into the equation to get our final answer.
y= -1/6x - 1
