Answer: y = 2x + 6
Step-by-step explanation:
Here the equation of line,
y = 2x + 1
y-intercept of the line is, (0, 1)
And, the slope of the line is 2.
Since, If a point (x,y) is dilated by a scale factor k about a point (a,b),
Then transformed point are get by,
[tex](x,y)\rightarrow (k(x-a)+a, k(y-b)+b)[/tex]
Thus, The transformed point of point (0,1) when dilation is occur by the scale factor 2 about the point (0,-4),
[tex](0,-4)\rightarrow (2(0-0)+0, 2(1+4)-4)[/tex]
[tex](0,-4)\rightarrow (0, 6)[/tex]
Thus, the point of the new line is (0,6)
And, the slope of the new line is 2 ( because in the dilation, the slope of the line does not change)
Thus, the equation of new line,
(y - 6) = 2 (x - 0)
y - 6 = 2x
y = 2x + 6
