The <em>rate of change</em> of a relationship is the <em>ratio of corresponding changes in value</em>. Symbolically, we indicate a change with the greek letter Δ (pronounced "delta"). A <em>change in x</em> is written Δx ("delta eks") and a <em>change in y</em> is written Δy ("delta why"). We're looking for the ratio Δy/Δx ("delta y over delta eks").
Mathematically, Δx and Δy are the <em>differences</em> between two corresponding x an y values. To pick these, we can take any two rows in our table. Let's pick rows 4 and 2, nice whole numbers:
We can confirm that this holds for every other pair, too - picking rows 2 and 1 as an example:
The two expressions are equivalent because the associative property of multiplication is applied, which means that no matter where you put the parenthesis, the two expressions will still be equal.