# Slope fields

##### Intros
###### Lessons
1. What are Slope Fields?
##### Examples
###### Lessons
1. Understanding Slope Fields
Find the directional field for the following equations:
1. $\frac{dy}{dx}=xy-x$
2. $\frac{dy}{dx}=\frac{x^2}{(y+1)}$
2. Determining the Equation from a Slope Field
Which equation best corresponds to the following slope field?

i.
$\frac{dy}{dx}=y-2$
ii.
$\frac{dy}{dx}=xy-2$
iii.
$\frac{dy}{dx}=x+1$
iv.
$\frac{dy}{dx}=-x+1$
1. Which equation best corresponds to the following slope field?

i.
$\frac{dy}{dx}=xy-2$
ii.
$\frac{dy}{dx}=-\frac{y}{x}$
iii.
$\frac{dy}{dx}=2x+y$
iv.
$\frac{dy}{dx}=xy-3$
1. Given the differential equation and its resulting slope field:
$\frac{dy}{dx}=\frac{y}{2}(y-3)$

Draw a solution to the following differential equation using the following initial value conditions:
1. $y(-2)=1$
2. $y(0)=4$
3. $y(1)=3$
###### Topic Notes
Slope fields, also called directional fields or vector fields, are graphical representations of first-order differential equations.

Slope Fields consist of a bunch of lines indicating the slope of y with respect to x, or $\frac{dy}{dx}$