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?

If a line is perpendicular to another, it means that the slope of the first line is equivalent to the negative reciprocal of the second line. In simple terms, that means the slope of the first line is the same as -1 over the slope of the perpendicular line (-1/m).So, we just need to do -1/-2 (as -2 is the slope of the perpendicular line) to work out the slope of the first line. -1/-2 is the same as 1/2, or 0.5.Now, we know the equation of the first line is y = 1/2x + b.We just need to substitute in the coordinates (6,1) respectively into the x and y values and we get:(1) = 1/2(6) + bNow let's simplify:1 = 3 + bNow we just need to find the y-intercept (which is b), and to do this, we just need to subtract 3 from both sides of the equation to isolate the b:1 - 3 = b-2 = bNow that we know our b value, we just have to rewrite the whole equation, and you'll have your answer:y = 1/2x - 2