Rate of Change Analyzer

Pre-Algebra · Axiom Academy

A line on a graph tells a story of change — and its slope is the narrator. Here is exactly what that slope measures, and why it reads off the rise over the run. 1. Slope Is the Rate of Change Suppose a morning starts at 60°F and warms by 2°F every hour . Plot temperature against time and you get a straight line. Walk along it one hour at a time: each step to the right (the run ) is matched by a fixed step upward (the rise ). That fixed rise-per-run is the slope — and here it is the warming rate itself. 2°F gained for every 1 hour — that is the rate of change The size of the slope tells you how fast the quantity changes. Compare two stores: one charges 3 per item , the other 7 per item . Both lines start at zero, but over the same run of 10 items the dearer store rises far higher — so its line is steeper . A bigger slope is a faster rate. Each item adds 3. After 10 items the total is 30 — a gentle climb. Each item adds 7. After 10 items the total is 70 — a steep climb. Over the identical 10-item run, the steeper line rises 70 instead of 30. More rise per run = steeper. Whenever one line is steeper than another, its quantity is changing at the faster rate. The 7-per-item line climbs more than twice as fast as the 3-per-item line, so it is more than twice as steep. Steepness on the page is a direct picture of how quickly the cost is piling up. 3. On a Distance–Time Graph, Slope Is Speed

This is the written version of the interactive lesson above. See the full Pre-Algebra course.