The equation of line t is y=12x+3. Line t' is the image of line t after a dilation with a scale factor of 3 centered at (–3,2).Which of these points lie on line t'? Select all that apply.(8,6)–7,–32(2,4)(–4,0)Submit

To find the points that lie on line t', we first need to understand how a dilation with a scale factor of 3 centered at (-3,2) would affect line t.

The equation of line t is y = 12x + 3. A dilation with a scale factor of 3 would multiply the y-coordinates of all points on line t by 3, but it would not affect the x-coordinates. However, because the dilation is centered at (-3,2), we also need to subtract 3 from the x-coordinates and 2 from the y-coordinates.

So, the equation of line t' after the dilation would be y = 12(x-3) + 3*3 = 12x - 36 + 9 = 12x - 27.

Now, we can check which of the given points satisfy this equation:

1. (8,6): 6 = 12*8 - 27 = 96 - 27 = 69. This point does not lie on line t'.

2. (-7,-32): -32 = 12*(-7) - 27 = -84 - 27 = -111. This point does not lie on line t'.

3. (2,4): 4 = 12*2 - 27 = 24 - 27 = -3. This point does not lie on line t'.

4. (-4,0): 0 = 12*(-4) - 27 = -48 - 27 = -75. This point does not lie on line t'.

So, none of the given points lie on line t'.