Given:
Equation of line is:
[tex]3x-5y=12[/tex]
The general equation of line is:
[tex]y=mx+c[/tex][tex]\begin{gathered} 3x-5y=12 \\ 5y=3x-12 \\ y=\frac{3}{5}x-\frac{12}{5} \end{gathered}[/tex]
Solpe of given line is:
[tex]m=\frac{3}{5}[/tex]
Slopes of two parallel line is equal then:
[tex]m_1=m_2=\frac{3}{5}[/tex]
General equation is:
[tex]\begin{gathered} y=mx+c \\ y=\frac{3}{5}x+c \end{gathered}[/tex]
Line pass through (20,-8) that mean:
[tex]\begin{gathered} x=20 \\ y=-8 \end{gathered}[/tex][tex]\begin{gathered} y=\frac{3}{5}x+c \\ -8=\frac{3}{5}\times20+c \\ -8=12+c \\ c=-20 \end{gathered}[/tex]
So the equation of line is:
[tex]\begin{gathered} y=mx+c \\ m=\frac{3}{5} \\ c=-20 \\ y=\frac{3}{5}x-20 \\ 5y=3x-100 \\ 3x-5y=100 \end{gathered}[/tex]
Equation of line is 3x-5y=100
