Inverse variation- A nonlinear relationship in which the product of two variables is constant. An inverse variation can be represented by an equation of y=kx, or xy=k where k is a constant.
Inverse Table
![Picture](/uploads/5/9/7/0/59700795/1445475512.png?250)
This is an Inverse table because the X-axis and Y-axis is not increasing or decreasing at a constant rate. You can find out if a table is inverse because the x and y axis cannot be a constant rate but they have to equal the same number when they are multiplied. Ex) 1 times 12 equals 12, and 2 times 6 equals 12.
Graph
![Picture](/uploads/5/9/7/0/59700795/1445476237.png?250)
This graph is an inverse graph. You can tell that this graph is inverse because it is decreasing but not at a constant rate. The graph is also curving while its decreasing because the graph isn't at a constant rate. The graph also does not touch the y-axis or the x-axis in the graph.
Inverse Equation
![Picture](/uploads/5/9/7/0/59700795/1445476706.png?250)
This equation is an inverse equation. Its an inverse equation because you would multiply the x by the y to get k. So each the x times the y would have to equal k. You could also do k divided by x equals y because any of the fact families work for this equation for inverse equations.
Ex) (1)(12)=12
(2)(6)=12
(3)(4)=12
Ex) (1)(12)=12
(2)(6)=12
(3)(4)=12
Parent Problem
Will is training for a marathon. He decides to increase his speed each day. He will start at 1 mph and increase his speed. Will, will start at 1 and go 2, 2.5, 4, 5, and 10 miles per hour to get to 20 miles each day. Make a table,graph, and equation on how long it will take Will to run in hours each day.
Parent Problem Table
Parent Problem Graph
Parent Problem Equation
My parents had no trouble on Inverse variation. They got all of the questions done in 1 try and thought it was easy.They new how to find out if it was inverse or linear and thought that the ,table,graph, and equation was easy.
Reflections
In this investigation I learned all about inverse variations. I learned that the x times the y must equal the same thing when multiplied to make the table or graph or equation inverse. I learned that the x and y axis never touch the x or y intercepts in inverse. I learned how to identify if a graph or table or equation is inverse from this book.
Photo used under Creative Commons from Keith Allison