Answer:
[tex]k=\frac{1}{2}[/tex]
Step-by-step 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
[tex]2y=x+8[/tex]
isolate the variable y
[tex]y=0.5x+4[/tex] ----> equation A
The slope of the line A is m=0.5
The y-intercept of the line A is b=4
Line B
[tex]y-\frac{1}{2}x=2[/tex]
isolate the variable y
[tex]y=\frac{1}{2}x+2[/tex] ----> 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
[tex]4k=2[/tex]
solve for k
[tex]k=\frac{1}{2}[/tex]
