Respuesta :

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

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