Question

Consider the line y = x . If the line is dilated by a factor of 1 3 , what is the equation of the resulting line? If the resulting line is translated 1 unit down, what is the equation of the resulting line?
Please help! I'll give ten points.

Answer 1

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

$y=x$

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,

$y=0$

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.

$y=x$

The translation is defined as

$y=x+b$

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.

$y=x-1$

Therefore, the equation of the resulting line is y=x-1.