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

Answer 1

`y=(1)/(3)x`

and

`y=(1)/(3)x-1`

Explanation:

When we dilate y = x by a factor of "a", we have the equation:

y = a*x

So, firstly, we need to dilate by a factor of 1/3, thus we would have:

`y=(1)/(3)x`

Now, whenever we have a line y = x, per say, if we want to translate "b" units up, we would have:

y = x + b

if we want to translate "b" units down, we have"

y = x - b

Now, since we have
`y=(1)/(3)x` and we want to translate "1" unit down, we will thus have:

`y=(1)/(3)x-1`