Finding the Image of a Line for Beginners

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In summary, the conversation is about a problem that involves finding the image of a line using linear transformations. The person is struggling because the book does not provide examples for this specific type of problem. They eventually figure out the solution, which involves finding expressions for x1 and x2 in terms of y1 and y2, substituting them into the line equation, and solving for the image of the line. They express frustration with the lack of explanation in the book and express relief upon finding the solution.
  • #1
Octavius1287
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Im stuck on this, the book has no examples on this kind of problem (and its the first one) And i learn mostly from examples

Im on b) and i can't figure out gow to get the image of the line
the back says the answer should be 9y1-4y2=6 and I've spent over a hour on this and I am not seeing it
IMG_20130320_115711_145_zps48df21c6.jpg
 
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  • #2
The first step is to find an expression for x1 and x2 in terms of y1 and y2.
 
  • #3
the book shows how to do that but only with 2 equation and putting them in matrix form then getting the inverse, i only have 1 equation. For this case its not explained and no example is given
 
  • #4
Octavius1287 said:
the book shows how to do that but only with 2 equation and putting them in matrix form then getting the inverse, i only have 1 equation.

I mean do it with the equations defining the linear transformation. There are two of those.
 
  • #5
ok i got
x1=(3/2)y1-(1/2)y2

x2=-2y1+y2
 
  • #6
Octavius1287 said:
ok i got
x1=(3/2)y1-(1/2)y2

x2=-2y1+y2

Great! Now substitute those into the line equation. That will give you the image of the line.
 
  • #7
oooh ok thanks. why can't the book just say that!
 

Related to Finding the Image of a Line for Beginners

What is the process of finding the image of a line?

The process of finding the image of a line involves identifying a point on the line, determining the slope of the line, and then using the slope to find other points on the line. These points can then be plotted on a coordinate plane to create the image of the line.

What is the importance of finding the image of a line?

Finding the image of a line is important in many areas of science and mathematics. It allows us to visualize and understand the behavior of a line in a given space, and can also be used to solve problems and make predictions.

What are the different methods for finding the image of a line?

There are several methods for finding the image of a line, including using the slope-intercept form, point-slope form, and standard form of a linear equation. These methods involve different approaches, but ultimately lead to the same result.

Can the image of a line be negative?

Yes, the image of a line can be negative. This can occur when the line has a negative slope, meaning it is decreasing as it moves from left to right on a coordinate plane.

What is the relationship between the image of a line and its equation?

The image of a line is directly related to its equation. The equation of a line can be used to determine its slope and y-intercept, which are important in finding the image of the line. Similarly, the image of a line can be used to create an equation that represents the line on a coordinate plane.

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