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?

! i'll give ten points.

The resulting equation after dilation: y=x.

The resulting equation after translation: y=x-1.

Step-by-step explanation:

The given equation of line

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,

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.

The translation is defined as

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.

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

exa:

)

3+11

14

step-by-step explanation:

from this example, we can see that subtracting with integers is the same as adding the opposite. we can solve using a number line or by using the saying "keep, change, change" to us solve. it is important to remember that we can subtract a negative and end up with a larger number than we started with.

30 feet

step-by-step explanation:

that would be 2 1/2 * 12

= 24 + 6

= 30 feet   (answer)