What is the equation of a line that passes through the point (6,1) and is perpendicular to the line whose equation is y=2x-6?

Y = (-1/2)x - 3
This line has a slope of -1/2.
Perpendicular lines have negative reciprocal slopes. The slope of the line perpendicular to the given line is 2.

y = mx + b is the slope-intercept form of the equation of a line
We have the point (6, -4) as a point on the given line. We can use these as the values of x and y in the slope-intercept form of the equation of a line.

-4 = 2(6) + b
-4 = 12 + b
-16 = b
This tells us that the line perpendicular to the given line has a y-intercept of -16. The equation of that line is:

y = 2x - 16