Parallel lines have same slope so so far the new equation looks like this
[tex]y = 1x + b \\ y = mx + b[/tex]
now you plug in you points or coordinates to find b or solve for the y-intercept
[tex] - 1 = 1(1) + b[/tex]
[tex] - 1 = 1 + b[/tex]
[tex] - 1 = 1 + b \\ - 1 = - 1[/tex]
[tex] - 2 = b[/tex]
now that you have your b your final solution is
[tex]y = 1x - 2 \: or \: y = x - 2[/tex]
