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Differential Equations

Differential Equations

At a Glance - 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", 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).

Example 1

The line below has a slope of 5.

Fill in the indicated number.


Example 2

The line below has a slope of 4.

Fill in the indicated number.


Example 3

The line below has a slope of -0.7. Find the indicated number.


Example 4

The function f is a line with slope . If f (a) = 3, what is ?


Example 5

The line below has a slope of 2. Find the indicated number.


Exercise 1

The line below has slope 3. Find the indicated number.


Exercise 2

The line below has slope . Find the indicated number.


Exercise 3

The line below has slope 0.2. Find the indicated number.


Exercise 4

Find the indicated number.


Exercise 5

Find the indicated number.


Exercise 6

The line below has slope . Find the indicated number.


Exercise 7

The line below has slope . Find the indicated number.


Exercise 8

The line below has slope -7. Find the indicated number.


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