ANSWER
[tex]y=-3x-7[/tex]EXPLANATION
We want to find the equation of the line passing through (-3, 2) and parallel to:
[tex]6x+2y=1[/tex]First, put the equation in slope intercept form:
[tex]\begin{gathered} 2y=-6x+1 \\ y=-3x+\frac{1}{2} \\ \text{where slope, m = -3} \\ in\text{tercept, b = }\frac{1}{2} \end{gathered}[/tex]A line that is parallel to another line has the same slope as that line.
Therefore, the slope of the required line is -3.
Now, use the point-slope method to find the equation of the line:
[tex]y-y1=m(x-x1)[/tex]where (x1, y1) is the point the line passes through
Therefore, the equation of the line is:
[tex]\begin{gathered} y-2=-3(x-(-3)) \\ y-2=-3(x+3) \\ y-2=-3x-9 \\ \Rightarrow y=-3x-9+2_{} \\ y=-3x-7 \end{gathered}[/tex]That is the equation of the line.
