Question

I need help with this math review question for finals

Answer 1

Given:

Equation of line is:

`3x-5y=12`

The general equation of line is:

`y=mx+c`
`\begin{gathered} 3x-5y=12 \\ 5y=3x-12 \\ y=(3)/(5)x-(12)/(5) \end{gathered}`

Solpe of given line is:

`m=(3)/(5)`

Slopes of two parallel line is equal then:

`m_1=m_2=(3)/(5)`

General equation is:

`\begin{gathered} y=mx+c \\ y=(3)/(5)x+c \end{gathered}`

Line pass through (20,-8) that mean:

`\begin{gathered} x=20 \\ y=-8 \end{gathered}`
`\begin{gathered} y=(3)/(5)x+c \\ -8=(3)/(5)*20+c \\ -8=12+c \\ c=-20 \end{gathered}`

So the equation of line is:

`\begin{gathered} y=mx+c \\ m=(3)/(5) \\ c=-20 \\ y=(3)/(5)x-20 \\ 5y=3x-100 \\ 3x-5y=100 \end{gathered}`

Equation of line is 3x-5y=100