derivatives Topics 7.3-7.4-Slope Fields undefined Important Ideas: slope field is a graphical representation of a differential equation that allows us to visualize the family of solution curves . making a slope field : - calculate the slope at various ordered barrs ( rise , run ) - noinkslaves using short line segments - easiest slopes to plot are slopeszo, or undef. ", or slope it ! at solution curves will follow the trend of the slopes and most rass through the initial condition it given #3 X Slop Check Your Understanding! 1. Draw a slope field for each differential equation. Each tick mark is one unit. O x y slove dy = -y slopez - y 10 dx y # # passes 2. Sketch the particular solution to - = -y that passes through (0, -1) on your slope field above. 3. The slope field of differential equation is shown below. Which of the following equations could be a specific solution to that differential equation? A ) y = ex B ) y = x2 C) y = Inx D) y = sin x 4. Let y = f (x) be a particular solution to the differential equation ay = = satisfying f (3) = 4. Write an equation of the line tangent to f (x) at x = 3. Use this line to approximate f (3.1). CALC MEDIC