Given the equation of the line :
[tex]4x-3y=-12[/tex]
To find the slope, solve the equation for y:
[tex]\begin{gathered} 4x-3y=-12 \\ -3y=-4x-12 \end{gathered}[/tex]
Divide both sides by -3 :
[tex]\begin{gathered} \frac{-3y}{-3}=\frac{-4x}{-3}-\frac{12}{-3} \\ \\ y=\frac{4}{3}x+4 \end{gathered}[/tex]
So, the slope of the given line = 4/3
And the slope of the line parallel to the given line = 4/3
Because the parallel line have the same slopes
So, the answer is : slope = 4/3
