The equation of the line given is,
[tex]y=-4x-3[/tex]
We were told that a line is parallel to the equation.
Therefore, from the equation above, the slope of the line is
[tex]m_1=-4[/tex]
Rule for paralel line
[tex]m_1=m_2[/tex]
Hence, the slope (m2) is
[tex]-4[/tex]
Also, the line passes through the point (-2,4).
The formula to calculate the equation in sope-intercept dform is,
[tex]y-y_1=m(x-x_1)[/tex]
where,
[tex](x_1,y_1)=(-2,4)[/tex]
Therefore,
[tex]y-4=-4(x-(-2))[/tex]
Simplify
[tex]\begin{gathered} y-4=-4(x+2) \\ y-4=-4x-8 \\ y=-4x-8+4 \\ y=-4x-4 \end{gathered}[/tex]
Hence, the equation of theline is
[tex]y=-4x-4\text{ \lparen Option 3\rparen}[/tex]
