a line that is parallel to a line whose equation is y = -4x + 2, has the same exact slope, [tex]\bf y=\stackrel{slope}{-4}x+2[/tex]
so, what's the equation of a line whose slope is -4 then, and passes through )(-6, -4)?
[tex]\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ -6}}\quad ,&{{ -4}})\quad
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies -4
\\\\\\
% point-slope intercept
y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-(-4)=-4[x-(-6)]\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y+4=-4(x+6)\implies \stackrel{point-slope~form}{y+4=-4x-24}
\\\\\\
y=-4x-24-4\implies \stackrel{slope-intercept~form}{y=-4x-28}[/tex]
