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.

Given parameters:

Coordinate of line 1 = P(3, -5) and Q(1, 4)

Coordinate of line 2 = R(-1, 1) and S(3, -3)

To know if the two lines are parallel, it must hold that both lines must have the same amount of slope.

Parallel lines are lines that do no intersect at any point.

So we must find the slope of the both lines given.

The formula of the slope of line is:

        Slope  =

For line 1,  P(3, -5) and Q(1, 4) and line 2 R(-1, 1) and S(3, -3)

      x₁ = 3,  y₁ = -5

      x₂ = 1,   y₂ = 4

So;

 Slope of line 1  =   =

For line 2 R(-1, 1) and S(3, -3)

      x₁ = -1,  y₁ = 1

      x₂ = 3,  y₂ = -3

Slope of line 2  =   =   = -1

Since both slopes are different, they are not parallel lines. Parallel lines have the same slope.