The equation of the line is given as
[tex]3x+4y=7[/tex]The general equation of a line is
[tex]\begin{gathered} y=mx+c \\ \text{where,} \\ m=\text{slope} \\ c=\text{intercept on the y a}\xi s \end{gathered}[/tex]Step 1: Make y the subject of the formula
[tex]3x+4y=7[/tex]Subtract 3x from both sides
[tex]\begin{gathered} 3x+4y=7 \\ 3x-3x+4y=7-3x \\ 4y=-3x+7 \end{gathered}[/tex]Step 2: Divide all through by 4
[tex]\begin{gathered} 4y=-3x+7 \\ \frac{4y}{4}=-\frac{3x}{4}+\frac{7}{4} \\ y=-\frac{3x}{4}+\frac{7}{4} \end{gathered}[/tex]Step 3 : Compare coefficients with the general equation of a line below
[tex]\begin{gathered} y=mx+c \\ y=-\frac{3x}{4}+\frac{7}{4} \\ \text{hence,} \\ m=-\frac{3}{4},c=\frac{7}{4} \end{gathered}[/tex]For a perpendicular line,
[tex]m_1\times m_2=-1[/tex]That is, we will have that
[tex]\begin{gathered} -\frac{3}{4}\times m_2=-1 \\ -\frac{3m_2}{4}=-1 \\ \text{cross multiply.} \\ -3m_2=-4 \\ \text{divide both sides by -3} \\ \frac{-3m_2}{-3}=\frac{-4}{-3} \\ m_2=\frac{4}{3} \end{gathered}[/tex]Hence,
The slope of the perpendicular line will be = 4/3
For a parallel line,
[tex]m_1=m_2[/tex]Therefore,
The slope of a parallel line will be = -3/4
