Line AB contains (0, 4) and (1, 6) Line CD contains points (2, 10) and (- 1, 4). Lines AB and CD are:
parallel because the slopes are the same.
perpendicular because the slopes are the same.
parallel because the product of the slopes is - 1.
perpendicular because the product of the slopes is - 1.

Solution:

The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line.

Line AB comprises points (0,4) and (1,6).

From these two points the slope of the line m₁ can be calculated as

m₁ = (y₂ - y₁) / (x₂ - x₁)

= (6 - 4) / (1 - 0)

= 2

Line CD comprises points (2,10) and (-1,4).

From these two points the slope of the line m₁ can be calculated as

m₂ = (y₂ - y₁) / (x₂ - x₁)

= (4 - 10) / (-1 - 2)

= -6 / -3

= 2

Since the slopes of Lines AB and CD are the same it can be concluded that the two lines are parallel.

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Line AB contains (0, 4) and (1, 6) Line CD contains points (2, 10) and (- 1, 4). Lines AB and CD are: parallel because the slopes are the same. perpendicular because the slopes are the same. parallel because the product of the slopes is - 1. perpendicular because the product of the slopes is - 1.

Summary:

The slope of the two lines is same and hence the lines are parallel.