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# 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*).