Question

Consider the line

y=x

If the line is dilated by a factor of 2, what is the equation of the resulting line?
If the resulting line is translated 3 units up, what is the equation of the resulting line?

Answer 1

y = 2x, y = 2x + 3

Explanation:

When a line is dilated by a factor of "a", we multiply that by "a".

So when we dilate y = x by a factor of 2, the resulting equation is:

y = 2*x

y = 2x

When we translate "b" units up the resulting equation would be

y = x + b

Since we have y = 2x, now we will translate 3 units up, so it becomes:

y = 2x + 3