Explanation
Step 1
remember the slope intercep form
[tex]y=mx+b[/tex]where m is the slope, and b is the y-intercept
so, we have
[tex]y=3x+1\rightarrow y=mx+b[/tex]hence,for the given line
slope=3
b=1
Step 2
2 lines are parallel if the slope is the same, so the slope of the line we are looking for is 3 too.
[tex]\begin{gathered} \text{if line 1}\parallel Line2 \\ \text{then} \\ \text{slope}_1=slope_2 \end{gathered}[/tex]therefore, we need a line that has
slope=3
and passes through (-3,-2)
we can use
[tex]\begin{gathered} y-y_1=slope(x-x_1) \\ \text{where} \\ \text{the point is(x}_{1,}y_1) \end{gathered}[/tex]replace
[tex]\begin{gathered} y-y_1=slope(x-x_1) \\ y-(-2)=3(x-(-3)) \\ y+2=3(x+3) \\ y+2=3x+9 \\ \text{subtract 2 in both sides} \\ y+2-2=3x+9-2 \\ y=3x+7 \end{gathered}[/tex]I hope this helps you
