Minimize Slope

Directions: Given the point (3,5), use digits 1-9, at most one time, to find a point (__, __) that minimizes the slope of the line that passes through the two points. The slope cannot be undefined.


How is the steepness of a line determined?

How do we calculate slope between two points? Explain which of the two slopes are steeper 1/9 or 9/1?

What does minimize mean?

Can you draw a picture that would help you find another point? Can you find another point?


Because of the vagueness of “minimize the slope”, here are two possible answers.

Points that minimize the slope: (9,6) or (9,4) if we think about the shallowest slope.

If we think about minimizing as the most left on the number line, then the here are the points that minimize the slope: (2,9) and (3,1)

Source: Nanette Johnson (Problem Based on Andrew Constantinescu’s Problem) and Andrew Constantinescu

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  1. Do you mean (4,1) as the last of the possible answers? (3,1) would be an undefined slope. And wouldn’t shallowest slope be 0. So (2,5), (4,5), (5,5), (6,5), (7,5), (8,5), or (9,5) would produce a shallower slope than (9,4) or (9,6).

  2. Why not (98,6) or (98,4)? Or even (98765321, 4)? I think the problem needs altering to state the the coordinate should have one digit only, if that’s the intention.

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