What equation do I write for a line that has a y intercept of 2 and is perpendicular to y=2/3x+4?

y = -3/2x + 2

Step-by-step explanation:

The equation has the format  y = mx + b  where  m  is the slope and  b  is the y-intercept.

The question gives you the y-intercept, so  b = 2.

As for the slope, you need the fact that perpendicular lines have slopes that are opposite ("negative") reciprocals of each other.

The slope of the line given in the question is 2/3.  The opposite reciprocal of 2/3  is  - 3/2.

The equation for the line is  y = -3/2x + 2