What is the equation of the ine perpendicular to 6x-2y=3 and passing through the point (5,−1)?

First we need to convert the equation to slope intercept form : y=mx+b, doing this, we get the equation of y = 3x - 3/2. following form of slope intercept, the slope is 3, With perpendicular lines, you take the opposite reciprocal of the slope (Just flip the denominator and the numerator = 3/1 to 1/3 then do the opposite of the new number = -1/3) Once we have the new slope we can then convert the equation into point slope form (y - y1 = m(x - x1)). You then get : 
y + 1 = -1/3(x - 5) Hope this helps :)