What is the equation of a line perpendicular to 8y-2x=-6 and also passing through the point (2,3).

We are asked to find the equation of a line perpendicular
to

8y-2x = -6 which passes through the point
(2,3).

We begin by finding the slope of the given line.  We
will convert the given equation to slope-intercept
form.

=>8y - 2x =
-6

=> 8y = 2x -
6

=> y = 2/8 x -
6/8

=> y = 1/4 x -
3/4

The slope of a line perpendicular to the above equation
would be -4.

We substitute -4 as the perpendicular slope
and the given point (2,3) into the slope intercept form to find
"b."

=>y = mx +
b

=> 3 = -4(2) +
b

=> 3 = -8 +
b

=> 11 = b

We now have
the slope and the y intercept for the equation of the perpendicular
line.

Substitute our values into the slope intercept
form.

y = mx + b

y = -4x +
11.

The answer is y = -4x + 11
(slope-intercept form).  The standard form of the answer is 4x + y =
11.