Question

A linear model passes through the points (20, 607) and (45, 1182). Find the equation of the line, with x as the input and y as the output.

Answer 1

A linear model passes through the points (20, 607) and (45, 1182).

`\begin{gathered} slope=(y_2-y_1)/(x_2-x_1) \\ x_2=45,x_1=20 \\ y_2=1182,y_1=607 \end{gathered}`
`\begin{gathered} m=(1182-607)/(45-20) \\ m=(575)/(25) \\ m=23 \end{gathered}`

The equation of the line, with x as the input and y as the output.

`\begin{gathered} (y-y_1)/(x-x_1)=m \\ (y-607)/(x-20)=23 \\ y-607=23(x-20) \\ y-607=23x-460 \\ y-23x-607+460=0 \\ y-23x-147=0 \\ y=23x+147 \end{gathered}`

The equation of the line is

`y=23x+147`