The equations for two lines in the coordinate plane are 2dx - y = - 4 and 4x - y = - 6, where d represents an unknown value. What value (s) of d would make these lines perpendicular?

First, let's put both lines in Slope-intercept form (y = mx + b) to make it a bit easier:

Line A:

2dx - y = - 4

-y = - 4 - 2dx

y = 2dx + 4

Line B:

4x - y = - 6

-y = - 6 - 4x

y = 4x + 6

We want a value for d so that line A is perpendicular to line B, which has a slope of 4. That means that the slope of line A must equal - 1/4.

2d = - 1/4

d = - 1/8