Question

The image shows lines AB and CD.
Are the 2 lines parallel? Explain or show your reasoning.

Answer 1

No

Explanation:

To classify the lines as "parallel", the distance between both x-intercepts must be equivalent to the distance between both y-intercepts. In this case, the lines are not parallel because the distance between both y-intercepts is different than the distance of both x-intercepts.

• Distance between two y-intercepts: 4 units
• Distance between two x-intercepts: 5 units

Since 4 ≠ 5, the lines are not parallel.

Answer 2

No, the lines are not parallel.

Explanation:

Parallel lines have the same slope.

Therefore, find the slopes of both lines and compare.

Slope formula

`\sf slope=(change\:in\:y)/(change\:in\:x)`

Line AB

A = (0, 6)

B = (8, 0)

`\implies \sf slope=(0-6)/(8-0)=-\frac34`

Line CD

C = (-3, 4)

D = (0, 2)

`\implies \sf slope=(2-4)/(0-(-3))=-\frac23`

As the slopes of the 2 lines are different, the lines are not parallel.