Answer :
Answer:
B) y = 5x -12
Step-by-step explanation:
Dilation changes the distance of points from the origin, but does not change angles (slopes of lines). Hence the y-intercept moves from -8 to 3/2·(-8) = -12, but the slope stays the same.
Answer:
The correct option is B.
Step-by-step explanation:
The given equation of line is
[tex]y=5x-8[/tex] .... (1)
The slope intercept form of a line is
[tex]y=mx+b[/tex] ..... (2)
where, m is slope and b is y-intercept.
From (1) and (2), we get
[tex]m=5,b=-8[/tex]
It means the slope of line is 5 and y-intercept is at (0,-8).
If a line dilated with a scale factor of 3/2 centered at the origin, then the slope of both lines are same and the relation between coordinates is
[tex](x,y)\rightarrow(\frac{3}{2}x, \frac{3}{2}y)[/tex]
[tex](0,-8)\rightarrow(\frac{3}{2}(0), \frac{3}{2}(-8))=(0,-12)[/tex]
The slope of dilated line is 5 and the y-intercept is at (0,-12). So, the equation of dilated line is
[tex]y=5x-12[/tex]
Therefore option B is correct.