please help!

Question

Is the line through points P (0,5) and Q (-1,8) parallel to the line through points R (3,3) and S(5,-1)?

Choices are: a.) No, the lines have unequal slopes.

b.) Yes, the lines are both vertical.

c.) Yes, the lines have equal slopes.

d.) No, one line has slope, the other has no slope.

Answer 1

Slope of the first line passing through (0,5) and (-1,8) say m1 = y2-y1/x2-x1

(x1, y1) = (0,5)

(x2,y2) = (-1, 8)

m1 = 8-5/-1-0

m1 = 3/-1

m1 = -1/3

Slope of the second line through (3,3) and (5,-1) say m2 = y2-y1/x2-x1

m2 = -1-3/5-3

m2 = -4/2

m2 = -2

The lines have unequal slopes.

Option a is correct answer.

Answer 2

Given that two points are

Slope of a line containing two points is

m = -13

Given that two points are

Slope of a line containing two points is

m = -2

Therefore the slopes are not equal so the lines are not parallel to each other (option a).

Comments

Observe the given coordinates of first line P (0,5) and Q (-1 , 8).