Interpret rate of change informally as how much one quantity changes for each change in another.
Compare two points to describe the change
Problem
Look at the points \((2,~5)\) and \((5,~11)\). Complete the statement: When \(x\) increases by \(3\), \(y\) by .
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What this problem is really about
The two coordinates must be compared in the same direction, from the first point to the second. Subtract first x from second x and first y from second y separately; the sign of the y-difference tells whether y rises or falls, while its magnitude fills the requested change. Keeping coordinate roles separate avoids substituting the x-change for the y-change.
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