Equations of Parallel Lines

Directions: Using the digits 1 to 9 at most one time each, fill in the blanks to create two distinct parallel lines.
__ x + __ y = __

__ x + __ y = __


What do the equations of parallel lines have in common?


There are many answers but the coefficients of x and y for each line must be multiples of each other.  For example, 2x + 3y = 5 and 4x + 6y = 7

Source: Bryan Anderson

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Directions: Using the digits 0 to 9 at most one time each and as many …


  1. There are six blanks but nine numbers. That formulation confuses me a bit.

    • I see your point, both Robert and I missed that. Clearer wording is needed.
      Maybe this would be better.

      Directions: Fill in the empty spaces so that you create two distinct parallel lines. You can choose any whole number 1 through 9, but can only use a number once.

  2. But parallel lines have the same slope. Why don’t they use this?

    • Thanks Howard. Hopefully they will have conceptual understanding and approach the problem that way. Unfortunately, many students approach it through brute force.

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