What is the equation of the line that is perpendicular to y = 2x – 4 and has a y-intercept of –2?

In this equation, 2x is the slope, and -4 is the y intercept. 
For a line to be perpendicular to this line, the slope must be the negative reciprocal of 2x (which means that, when multiplied together, it equals one). 

The negative reciprocal of 2x is -x, so that is the slope of the new line. 

Now you just put -2 in for the y intercept, and you get: 

y = -x - 2