Question

Consider the line y=x

a. if the line is dilated by a factor of 2 what is the equation of the resulting line?
b. if the resulting line is translated 3 units up what is the equation of the resulting line? ​

Answer 1

a.
`y=2x`

b.
`y=2x+3`

Explanation:

We are given that a line

`y=x`

a. We have to find the equation of resulting line when the given line is dilated by a factor of 2.

We know that when a line is dilated by a then equation of line is given by

`y=ax`

We have a=2

Then, equation of line after dilation

`y=2x`

b.We have to find the equation of line when resulting line is translated 3 units up

Transformation rule when the y shift 3 units upward is given by

`(x,y)\righarrow (x,y+3)`

When the line
`y=2x` is translated 3 units up then the equation of line is given by

`y=2x+3`