# Differential Equations

### Topics

## Introduction to Differential Equations - At A Glance:

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*).

#### 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 |

#### 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.