Interpret rate of change informally as how much one quantity changes for each change in another.
Turn graph movement into a rate statement
Problem
A graph movement goes \(1~\text{unit}\) right and \(2~\text{units}\) up. Calculate \(\Delta~y\) per \(1\text{-}\text{unit}\) increase in \(x\), including its sign.
Translate the graph’s movement into signed changes before forming a rate: right is positive x and up is positive y. Divide the vertical change by the horizontal change so the result describes y-units per one x-unit, then use the line’s rising or falling direction as a sign check. This keeps the ratio’s order, sign, and units aligned.
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