Trying to make sense of maximum range

About 12:09 into this video, they start talking about Endurance and RangeSince the vertical axis is the "fuel usage rate" (how quickly you're using up fuel), it makes a lot of sense that the minimum point on the red line would be the speed at which you have maximum endurance.What I'm trying to understand is why the point of intersection between the reference line and the red line is the point of maximum range.I think I have an idea why, though I'm not sure if my intuition is correct.I took inspiration from what they mentioned later on about the effect altitude has on range.When altitude increases, your maximum range doesn't change (assuming ideal conditions). The red line (I think of it as the aircraft's range performance profile) is shifted along the reference line. The speed for range is increased/decreased by some factor (call it K), but the fuel usage rate is increased/decreased by that exact same factor K. For example, your speed doubles but your fuel usage rate also doubles. In fact, if you were to plot a graph of range vs. speed between the 2 shifted red lines (shifted range performance profiles), they would look (and be) exactly the same.I think of the reference line as described by Y = M * X, where Y = fuel usage rate, X = speed, and M being some constant of proportionality. From here, it's clear to see that the closer M is to 0, the better the range: more speed given a certain fuel usage rate, more distance covered in a given amount of time.If an aircraft had the performance profile described by Y = M * X, then regardless of what speed or fuel usage rate (both correspond to each other) the plane is at, it would always be at its maximum range. So there is no speed to fly at that will you give the best range, any speed will work.Imagine slowly rotating counter-clockwise (from the positive X axis to the positive Y axis) the reference line around the origin (point 0, 0) - this is similar to increasing M in Y = M * X. That point where this reference line "hits" the red line (aircraft's range performance profile) is the point where you get the best range out of the aircraft.Does this make sense? Or is my thinking wrong somewhere?