If the line is parallel to:
[tex]y=-3x+4[/tex]the we know that the slope is:
[tex]m=-3[/tex]Now we can replace the coordinate (1,1) in the line equation to find b so:
[tex]\begin{gathered} y=-3x+b \\ 1=-3(1)+b \\ b=1+3 \\ b=4 \end{gathered}[/tex]So the final equation is:
[tex]y=-3x+4[/tex]