Question

Line BC is represented by 3x + 2y = 8. Line AD is represented by –3x – 2y = 6. What is the relationship of line BC to line AD? Explain how the sum of the equations demonstrates this relationship.

Answer 1

Sample Response: Line BC is parallel to line AD. The system of equations has the sum 0 = 14. Since this is a false equation, the system has no solution, which means the lines will never intersect.

Answer 2

The correct answer for this question is this one:

The equations are:
BC: 3x + 2y = 8.
The slope of line BC is -3/2
y = -3/2 + 4

AD: –3x – 2y = 6.
The slope of line AD is -3/2
y = -3/2x - 3
So the relationship of the two lines is parallel lines.

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