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How to quickly find the specific data of 2 points that the slope meets the requirements?

For example,

dt = Open( "$SAMPLE_DATA/US Demographics.jmp" );

the "Eighth Grade Math" of this file is listed as the Y-axis and the "High School Graduates" is listed as the X-axis.
Identify two points that meet the following requirements:
The slope of their line is less than 0;
By extending their lines to the far right of the X-axis, the resulting Y-axis value is the largest
Just like the two points in the red line in the picture
How to find them using JSL.
How can this process be more efficient by using continuous circular comparisons?

Thanks!

Scripting

Re: How to quickly find the specific data of 2 points that the slope meets the requirements?

Are you looking for convex hull? check out @danschikore 's talk .

Re: How to quickly find the specific data of 2 points that the slope meets the requirements?

Thanks for the examples provided by Craige, I look at the imitation to solve this topic.
Thank Craige!

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