Question

Is the line through points P(-7,2) and Q(7,-6) parallel to the line through points R(14,0) and S(7,4). How do you know?

Yes; both lines are vertical
Yes, the lines have equal slopes
No; the lines have unequal slopes
No, one line has a zero slope and the other has no slopes

Answer 1

The lines through points P(-7,2) and Q(7,-6) and through points R(14,0) and S(7,4) are indeed parallel because they both have equal slopes of -4/7.

Step-by-step explanation:

To determine if the line through points P(-7,2) and Q(7,-6) is parallel to the line through points R(14,0) and S(7,4), we need to compare the slopes of the two lines. If the slopes are equal, the lines are parallel.

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula m = (y2 - y1) / (x2 - x1). For the line through points P and Q, the slope is m = (-6 - 2) / (7 - (-7)) = -8 / 14 = -4/7. For the line through points R and S, the slope is m = (4 - 0) / (7 - 14) = 4 / -7 = -4/7.

Since both lines have the slope of -4/7, we can conclude that the lines are parallel. Therefore, the correct answer is 'Yes, the lines have equal slopes.'