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

### 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?

Can you find another point?

Can you find another point?

### Answer

Points that maximize the slope: (4,9) and (2,1)

Source: Andrew Constantinescu

(2,6)

Nope, this answer is wrong. Please think it over once more.

(3,2)

2,1

How did you get this answer? I have a similar question but instead with the digits (2,5) and I have no idea how to solve it.

(2,5) would give you a slope of zero when paired with the given point (3,5). I approached this by trying to find a y-value that has the greatest distance from 5 and the x-value that is closest to 3.

When we talk about maximizing the slope are we talking about the number slope or the steepness. Because if we are talking about steepness (4, 1) and (2, 9) would also work. My students and I have had great discussions on this.

This is a really good point! I was thinking about the number, but I love the idea of talking about steepness and how it compares to the number for slope.

I enjoyed thinking about the extension of allowing the use of negatives as well as using the digits in decimal places! Conditions of the original task don’t limit this.

Nice! I love your idea.