Is the line through points P(3,-5) and Q(1,4) parallel to the line through points R(-1,1) and S(3-3)? Explain please.

To determine if the line through points P(3, -5) and Q(1, 4) is parallel to the line through points R(-1, 1) and S(3, -3), we need to compare the slopes of the two lines.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

For the first line passing through P(3, -5) and Q(1, 4), the slope is:

slope1 = (4 - (-5)) / (1 - 3) = 9 / (-2) = -9/2

For the second line passing through R(-1, 1) and S(3, -3), the slope is:

slope2 = (-3 - 1) / (3 - (-1)) = -4 / 4 = -1

Since the slopes of the two lines are not equal (-9/2 ≠ -1), the lines are not parallel.

To determine if the line through points P(3, -5) and Q(1, 4) is parallel to the line through points R(-1, 1) and S(3, -3), we can compare their slopes.

The slope of a line can be calculated using the formula:

slope = (change in y-coordinates)/(change in x-coordinates)

For the line through points P(3, -5) and Q(1, 4):
change in y-coordinates = 4 - (-5) = 9
change in x-coordinates = 1 - 3 = -2

Therefore, the slope of the line through P and Q is 9/-2 or -9/2.

For the line through points R(-1, 1) and S(3, -3):
change in y-coordinates = -3 - 1 = -4
change in x-coordinates = 3 - (-1) = 4

Therefore, the slope of the line through R and S is -4/4 or -1.

If two lines are parallel, their slopes should be equal.

In this case, the slope of the line through P and Q is -9/2, while the slope of the line through R and S is -1. Since these slopes are not equal, we can conclude that the line through P and Q is not parallel to the line through R and S.

whats the rule for:

56.38,51.28,46.18,41.08

PQ has slope -2/9

RS has slope -1
not parallel

rule: subtract 5.10 each time