Answer:
The resulting equation after dilation: y=x.
The resulting equation after translation: y=x-1.
Step-by-step explanation:
The given equation of line
[tex]y=x[/tex]
If a line passes through the center of dilation and dilated by factor k, then the equation of line is remains same.
It is given that the line is dilated by a factor of 1/3. The center of dilation is not given so the center of dilation is (0,0).
At x=0,
[tex]y=0[/tex]
It means the line passes through the point (0,0). Since the line passes through the center of dilation, therefore the equation of line is remains same.
[tex]y=x[/tex]
The translation is defined as
[tex]y=x+b[/tex]
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
The resulting line is translated 1 unit down.
[tex]y=x-1[/tex]
Therefore, the equation of the resulting line is y=x-1.
