The total distance of a trip is 986 miles and each hour they will drive 65 miles. write an equation to represent the number of remaining miles (y) after driving any number of hours (x)

Since X is any number of hours, finding the distance traveled would be represented as 65x. To find the remaining, you would need to subtract, so it'd look like this: 986-65x. The best thing to do with problems like these is to take it slowly, and highlight the important parts if possible!

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'.