Writing the slope-intercept form of a linear equation, we have:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Since parallel lines have the same slope, we can see that the slope of the line y = 2/3x + 1 is equal m = 2/3, so for our equation we also have m = 2/3.
Now, using the point (0, -4), we have:
[tex]\begin{gathered} y=\frac{2}{3}x+b \\ (0,-4)\colon \\ -4=\frac{2}{3}\cdot0+b \\ b+0=-4 \\ b=-4 \end{gathered}[/tex]So our equation is:
[tex]y=\frac{2}{3}x-4[/tex]y = 2/3x - 4
