There are several ways to answer this question.
1. Subtract x from both sides of the first equation to get 12 = y-x. Compare that to the second equation -8 = y-x. The coefficients of y and x are identical in each case, so the lines are parallel.
2. Write the equations in the form y=mx+b. The first equation is already in that form, where m=1 and b=12. The second equation needs to have x added to both sides to give y=x-8, so m=1 and b=-8. These are in the "slope-intercept" form, where the slope of both lines is m=1. Equal slopes mean the lines are parallel.
3. Compute y for some values of x. You will find in every case that the y value computed by the second equation is exactly 20 less than the y value computed by the first equation. That means all of the points on the second line are 20 units below the corresponding points on the first line. When two lines have the distance between them the same everywhere, they are parallel.
1. Subtract x from both sides of the first equation to get 12 = y-x. Compare that to the second equation -8 = y-x. The coefficients of y and x are identical in each case, so the lines are parallel.
2. Write the equations in the form y=mx+b. The first equation is already in that form, where m=1 and b=12. The second equation needs to have x added to both sides to give y=x-8, so m=1 and b=-8. These are in the "slope-intercept" form, where the slope of both lines is m=1. Equal slopes mean the lines are parallel.
3. Compute y for some values of x. You will find in every case that the y value computed by the second equation is exactly 20 less than the y value computed by the first equation. That means all of the points on the second line are 20 units below the corresponding points on the first line. When two lines have the distance between them the same everywhere, they are parallel.
