Solving for x-intercept
Substitute y = 0 to solve for the x-intercept.
[tex]\begin{gathered} y+3=2(x+3) \\ 0+3=2(x+3) \\ 3=2x+6 \\ 3-6=2x \\ -3=2x \\ 2x=-3 \\ \frac{2x}{2}=\frac{-3}{2} \\ x=-\frac{3}{2} \\ \\ \text{Therefore, the }x\text{-intercept is at }(-\frac{3}{2},0). \end{gathered}[/tex]Solving for y-intercept
Substitute x = 0 to solve for y-intercept
[tex]\begin{gathered} y+3=2(x+3) \\ y+3=2(0+3) \\ y+3=2(3) \\ y+3=6 \\ y=6-3 \\ y=3 \\ \\ \text{Therefore, the }y\text{-intercept is at }(0,3). \end{gathered}[/tex]