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Differential Equations

Differential Equations

Slopes (Again)

We know that the slope of a line is given by

or by

Since y is usually the dependent variable and x is usually the independent variable, you may also see

or

The symbol Δ is the Greek capital letter "Delta" (have button to click to hear delta pronounced), which mathematicians use to mean "change."

We usually use the slope formula to calculate the slope of a line given Δ y and Δ x. If we know the slope and Δ x we can instead use the slope formula to find Δ y.

Using algebra, if

then multiplying both sides by Δ x we get

Therefore if we know the slope of a line and we move over by Δ , then we know y is needs to to change by (slope × Δ x).

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