Final answer:
The lines represented by the equations y = x - 3 and x - y = 8 are parallel to each other because they both have the same slope of 1.
Step-by-step explanation:
To determine if the given lines y = x - 3 and x - y = 8 are parallel, perpendicular, or neither, one must first put both equations into slope-intercept form, or y = mx + b, where m represents the slope and b represents the y-intercept.
The first equation is already in slope-intercept form (y = x - 3) with a slope of 1.
To put the second equation in slope-intercept form, we solve for y:
- x - y = 8
- - y = -x + 8
- y = x - 8
The second equation also has a slope of 1.
Since both lines have the same slope, they are parallel to each other. Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. In this case, both slopes are 1, and not negative reciprocals, hence the lines are not perpendicular but parallel.
Using additional reference material provided on slopes and lines, we understand that if lines have the same slope and different y-intercepts, they are parallel and will never intersect. This principle confirms that the two lines in question are indeed parallel.