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

Solution

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

$\begin{gathered} slope=\frac{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=\frac{1182-607}{45-20} \\ m=\frac{575}{25} \\ m=23 \end{gathered}$

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

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

The equation of the line is

$y=23x+147$