how do I determine what equation is perpendicular to y=2x-4

Question

how do I solve which equation is perpendicular to y=2x-4

Answer 1

y = 2x - 4    Since this equation is in slope-intercept form, the slope of the line is 2.  Perpendicular lines have slopes that are negative reciprocals of each other.  Thus, the slope of a line perpendicular to this line would be -1/2.

So, any equation of the form y = -1/2 x + b would be an answer.

Answer 2

Well, it is already in the slope intercept form.. That, y=mx+b. In this problem, m=2 and b= -4 .  Any line whose is the negative reciprocal of 2 is perpendicular to this line.  

Now, you might ask, what is a negative reciprocal? In simple terms, change the sign of the number and turn it up side down.  How do turn 2 upside down? Simple put a one underneath it so it becomes 2/1. Now, 2/1 upside down is 1/2. Next, change the sign. Since it used to be positive, turn it into a negative. So, instead of having 1/2, now you have -1/2.  In conclusion, any equation that has a -1/2 for its b term is perpendicular to y= 2x +4.  Example y= -1/2x -19 or y= -1/2x +5.. Thats how simple it is.  Hope this helped.