An explanation please?

[Dionysus22]

Could somebody please show me how to do this:

f is the transformation (x,y) -> (x',y') where

x' = -5x - 6y
y' = 4x + 3y

L is the line x - 9y = 2

Find the equation of f(L), the image of L under f...

[HallsofIvy]

Could somebody please show me how to do this:

f is the transformation (x,y) -> (x',y') where

x' = -5x - 6y
y' = 4x + 3y

L is the line x - 9y = 2

Find the equation of f(L), the image of L under f...
You want to be able to replace the x and y in the equation of the line by x' and y' so you need to "invert" the transformation. Solve the two equation for x and y in terms of x' and y' .

Since linear transformations map lines into lines, another perfectly legitimate way to do this is: pick two points on L (pick whatever value you want for y and solve for x). Apply the transformation to each of those points to get two new points on F(L). Find the equation of the line through those two new points.