Mrs. Bryant, the principal at Dayton Middle School, asked her teachers to participate in a study on teaching methods. The 2 teachers who volunteered took part in a day-long study. Is this a random sample of the teachers in the school?

No, it isn't.

Step-by-step explanation:

A random sampling is one whereby every individual or possible member of a population or large sample has an equal chance of bein selected. Either the participants wants to be a part of the sample or not isn't taken into consideration, each and every member just has an equal Chance of being chosen. Volunteering isn't a random sampling protocol or procedure. By making Selection through volunteering, teachers who are more interested in the program are likely to show more interest, hence availing themselves for the programme. A random selection gives every possible subject an equal chance.

it has the same slope and a different y-intercept

hope this : )

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'.