For the equation of a line of the form y = mx + b, m is the slope and b is the intercept.
Thus the slope (m) for the line y = 6x + 1 is 6.
The slope of a line perpendicular to a line with slope m is -1/m, so the slope of the line perpendicular to y = 6x + 1 is -1/6.
For determining the equation of the line perpendicular to y = 6x + 1, we need to determine the y-intercept (b).
To do that we substitute the given (x,y) = (5,5) which the line passes through and the determined slope (m) - 1/6 into the y = mx + b equation as follows:
y = mx + b
5 = (-1/6)(5) + b
30/6 = -5/6 + b
35/6 = b
so equation is:
y = -1/6(x) + 35/6
