What is the equation of the line 2x + 3y = -6 after a dilation of 1/2 centered at the origin?

Answer 1

x-intercept of original: let y = 0, x = -3
y-intercept of original: let x = 0, y = -2
So the new y-intercept must be -1
and of course the slope does not change
we would have
2x + 3y = c
sub in (0,-1)
0 - 3 = c

the new equation is 2x + 3y = -3

Answer 2

You start with 2x + 3y = -6
after applying the dilation of 1/2, all the x- and y- values are 1/2 as big.
So, using the new values,
2(x/2) + 3(y/2) = 1/2 (2x+3y) = 1/2(-6)
So now,
2x+3y = -3