The lines shown below are perpendicular. if the green line has a slope of 1/7, what is the slope of the red line?

Perpendicular lines have negative reciprocal slopes. All that means is " flip " the slope and change the sign. Example : if you have a slope that is 3/4 and you want to find the perpendicular slope, just flip the slope 4/3 and change the sign - 4/3. 3/4 and - 4/3 are perpendicular. So basically, you need to find the negative reciprocal of - 2/3. So flip the slope and change the sign and what do you get?

perpendicular slope would be 3/2