Question

The line represented by 2y = x + 8 is dilated by a scale factor of k centered at the origin, such that the image of the line has an equation of y - 12x = 2. What is the scale factor?

Answer 1

`k=(1)/(2)`

Explanation:

we know that

A dilation is a non rigid transformation that produce similar figures

If two lines are similar, then the lines are parallel

Lines parallel have the same slope

so

we have

Line A

`2y=x+8`

isolate the variable y

`y=0.5x+4` ----> equation A

The slope of the line A is m=0.5

The y-intercept of the line A is b=4

Line B

`y-(1)/(2)x=2`

isolate the variable y

`y=(1)/(2)x+2` ----> equation B

The slope of the line B is m=0.5

The y-intercept of the line B is b=2

Remember that

The y-intercept of line A multiplied by the scale factor k must be equal to the y-intercept of line B

so

`4k=2`

solve for k

`k=(1)/(2)`