Respuesta :
Answer:
[tex]y=2x+8[/tex]
Step-by-step explanation:
Given:
The original equation of the line 'l' is given as:
[tex]y=2x+2[/tex]
Scale factor of dilation is, [tex]k=4[/tex]
Now, when a line is dilated by some scale factor 'k' centered at the origin, then the parallelism of the line is reserved and only the y intercept changes.
The rule of dilation for a point [tex](x,y)[/tex] with a scale factor 'k' is given as:
[tex](x,y)\rightarrow (kx,ky)[/tex]
The standard form of a line is of the form [tex]y=mx+b[/tex], where, 'm' is the slope and 'b' is the y-intercept of the line. On comparing the line 'l' with the standard form, we get:
[tex]Slope,m=2\\y-intercept,b=2[/tex]
The y-intercept is at the point (0, 2). Now, applying dilation rules on this point, we get:
[tex](0,2)\rightarrow (4\times 0,4\times 2)=(0,8)[/tex]
So, the new y-intercept after dilation is at (0, 8) or the new value of 'b' is 8.
Therefore, the dilated line equation is given as:
[tex]y=mx+b\\y=2x+8[/tex]
