A useful fluid value is a straight line only between two chosen viewport widths. Below the first point it should stay at the lower bound; above the second it should stay at the upper bound. CSS clamp() expresses those three regions in one value when its preferred expression contains the correct slope and intercept.
Find the exact slope between the points
Let the small point be viewport V1 with value S1 and the large point V2 with value S2. The slope in pixels of value per pixel of viewport is (S2 − S1) / (V2 − V1). For 320px → 16px and 1200px → 32px, the exact slope is 16/880, or 1/55. Keeping this as a rational number avoids binary floating-point drift before the final CSS text is formatted.
Move the line back to a zero-width intercept
The pixel intercept is S1 − slope × V1. It does not mean a real design should use that value at a zero-pixel viewport; it is simply the constant term needed for the line to pass through both selected points. In the example, the intercept is 560/55px, about 10.181818px. Dividing by a 16px root yields about 0.636364rem.
Convert the slope into a vw coefficient
One vw equals one percent of the viewport width, so the slope must be multiplied by 100 before it is written beside vw. The example coefficient is 100/55, about 1.818182vw. Combined with the rem intercept and bounded by 1rem and 2rem, the copied value is clamp(1rem, 0.636364rem + 1.818182vw, 2rem). The decimal text is an approximation of the exact rational line, which is why endpoint verification matters.