Finding Inverses of Linear Equations and Graphs
Description/Explanation/Highlights
Video Description
This video explains how to find inverses of linear equations and graphs.
Steps and Key Points to Remember
To find inverses of linear graphs and equations, follow these steps:
- To find the inverse of a linear graph, use y = mx + b, where m is the slope of the line and b is the y-intercept, to write the equation of the original line. For example if the slope (rise over run) is \(\frac{1}{2}\) and the line crosses the y-axis at 2 the equation of the line is: \(y=\frac{1}{2}x+2\)
- Make a table of a few of the x-values on the line and using the equation you just found, find the related y-values.
- Make a new table and write the y-values in the x column and the x-values in the y column. In other words switch x & y.
- Graph the values in the new table and connect the points with a line. You have graphed the inverse of the original line!
- This new inverse line should be a reflection of the original line over the graph of the y = x line.
- You can also solve the equation algebraically for its inverse equation by switching x & y creating this new equation: \(x=\frac{1}{2}y+2\)
- Now, solve the new equation for y by subtracting 2 from both sides and multiplying by 2 to get rid of the fraction. This is the equation of the inverse line. \(y=2x-4\)
- In function notation the inverse is written as: \(f ^{-1}(x)=2x-4\) and is read “f inverse of x equals 2x minus 4.”
Here are some key points to keep in mind when finding inverses:
- Inverse graphs reflect over the y = x line.
- To graph an inverse, make a table of the coordinates of key points and switch the x & y values. Graph the switched coordinates to graph the inverse.
- To find the inverse equation for a linear graph, use Y = mx + b to write the equation of the original line. Switch x and y in the equation and solve the new equation for Y. This is the inverse equation.
- \(f^{-1}(x)\) is used as the notation for inverse.
Video Highlights
- 00:00 Introduction and definitions
00:30 Inverse example of graph of \(y = \frac{1}{2}x + 2\)
04:55 Finding inverse of \(y = \frac{1}{2}x + 2\) algebraically
06:12 Finding inverse of \(y=4x-8\)
07:52 Conclusion
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