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  "body": "\n## Statement\n\nLet $I$ be an interval and let $f \\colon I \\to \\mathbb{R}$ be [[convex|0VV0HSW1ZS]].\nThen for all $x \u003c y \u003c z$ in $I$,\n$$\\frac{f(y) - f(x)}{y - x} \\le \\frac{f(z) - f(x)}{z - x} \\le \\frac{f(z) - f(y)}{z - y}.$$\n\n## Remarks\n\nWrite $y = t x + (1 - t) z$ with $t = (z - y)/(z - x)$, and apply the definition of convexity.\nThe converse holds: a function with this property is convex.\nThe first and the last quotient give the adjacent form `ConvexOn.slope_mono_adjacent` of Mathlib.\n\n## Explanations\n\n### L1 human\n\nFor a convex function, chords further to the right are steeper.\nSo the slopes of the graph increase from left to right.\n",
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