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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.

Hint

Hint

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?

Answer

Answer

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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