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?(1 point) Responses Yes; both lines are vertical Yes; both lines are vertical Yes, the lines have equal slopes Yes, the lines have equal slopes No; the lines have unequal slopes No; the lines have unequal slopes No, one line has a zero slope and the other has no slop
No, one line has a zero slope and the other has no slope. The line through points P(-7,2) and Q(7,-6) has a slope of (2 - (-6)) / (-7 - 7) = -8/14 = -4/7. The line through points R(14,0) and S(7,4) has a slope of (0 - 4) / (14 - 7) = -4/7. Since the slopes of the two lines are not equal, they are not parallel.
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 lines.
The formula to calculate the slope of a line passing through two points (x1, y1) and (x2, y2) is:
slope = (y2 - y1) / (x2 - x1)
For the line passing through P(-7,2) and Q(7,-6):
slope_PQ = (-6 - 2) / (7 - (-7))
slope_PQ = -8 / 14
slope_PQ = -4/7
For the line passing through R(14,0) and S(7,4):
slope_RS = (4 - 0) / (7 - 14)
slope_RS = 4 / -7
slope_RS = -4/7
Since the slopes of both lines are equal (-4/7), we can conclude that 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).
Therefore, the correct answer is:
Yes, the lines have equal slopes.
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 their slopes.
The slope of a line can be found using the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
Let's calculate the slope of each line:
For the line through points P(-7,2) and Q(7,-6):
slope = (-6 - 2) / (7 - (-7))
= (-8) / (7 + 7)
= (-8) / 14
= -4/7
For the line through points R(14,0) and S(7,4):
slope = (4 - 0) / (7 - 14)
= 4 / (-7)
= -4/7
Since the slopes of both lines are the same (-4/7), we can conclude that the lines are parallel. Therefore, the correct answer is: Yes, the lines have equal slopes. (1 point)