Please help me with these problems and please show all work and steps to your solutions. This will help me better understand the problems once I have the answer and the steps for it. Thanks!
Please show work
1. How do we write the equation of a horizontal line? What would be an example?
2. How do we write the equation of a vertical line? What would be an example?
3. The points (3, 9), (5, 13), (15, 33), (34, 71), (678, 1359), and (1234, 2471) all lie on line M.
The points (3, -9), (5, -11), (15, -21), (34, -40), (678, -684), and (1234, -1240) all lie on line N.
a. Form the equations of both the lines. Show your work.
b. What are the co-ordinates of the point of intersection of lines M and N?
c. Write the co-ordinates of the intersections of lines M and N with the x-axis.
d. Write the co-ordinates of the intersection of lines M and N with the y-axis.
This provides explanations of working with writing equations of lines and finding intersection points.
Differential Equations : Phase Lines and Bifurcation Diagrams
Please see the attached file for the fully formatted problems.
22. (a) Use PhaseLines to investigate the bifurcation diagram for the differential equation
where a is a parameter. Describe the different types of phase lines that occur.
(b) What are the bifurcation values for the one-parameter family in part (a)?
(c) Use PhaseLines to investigate the bifurcation diagram for the differential equation
where r is a positive parameter. How does the bifurcation diagram change from the r = 0 case (see part (a))?
(d) Suppose r is negative in the equation in part (c). How does the bifurcation diagram change?