The slope of a line is 2/3 . what is the slope of a line that is perpendicular to this line?
a. -3/2
b. -2/3
c. 2/3
d. 3/2

The perpendicular line would have a slope of A) -3/2.

Perpendicular lines have opposite and reciprocal slopes.

To do the opposite, take the original slope (2/3) and change the sign (-2/3).

To do the reciprocal, take the slope we changed (-2/3) and flip it as a fraction (-3/2).

This gives us a new slope of -3/2.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.