To determine the slope and the relationship of these two different lines, let's convert both equations to slope-intercept form first.
[tex]y=mx+b[/tex]where m = slope and b = y-intercept.
Let's convert the first equation first.
[tex]\begin{gathered} 4y=-3x+48 \\ \text{Divide both sides by 4.} \\ \frac{4y}{4}=\frac{-3x}{4}+\frac{48}{4} \\ y=-\frac{3}{4}x+12 \end{gathered}[/tex]The slope of the first equation is -3/4.
Let's convert the second equation.
[tex]\begin{gathered} 3x+4y=-36 \\ 4y=-3x-36 \\ \text{Divide both sides by 4.} \\ \frac{4y}{4}=\frac{-3x}{4}-\frac{36}{4} \\ y=-\frac{3}{4}x-9 \end{gathered}[/tex]The slope of the second equation is also -3/4.
Since the slopes of the two lines are the same, they are parallel to each other. (relationship of the two lines)
