Answer:
The slope-intercept form of the equation of the line described is;
[tex]y=3x+1[/tex]Explanation:
We want to write the slope-intercept form of an equation that passes through the point;
[tex](-1,-2)[/tex]and parallel to the line;
[tex]y=3x+2[/tex]Since the line is parallel to each other, it means they will have the same slope;
[tex]m_1=m_2=3[/tex]Using the point slope formula to generate the equation;
[tex]y-y_1=m(x-x_1)[/tex]substituting the given point and slope we have;
[tex]\begin{gathered} y-(-2)=3(x-(-1)) \\ y+2=3(x+1) \\ y+2=3x+3 \\ y=3x+3-2 \\ y=3x+1 \end{gathered}[/tex]Therefore, the slope-intercept form of the equation of the line described is;
[tex]y=3x+1[/tex]