Insert the two points into the general line equation:

$y=mx+t\{y\}=\{mx\}+\{t\}$

Use the addition method.

Compute $1)+2)1)\backslash ;+\backslash ;2)\backslash ;$.

Plug $mm$ into one of the two functions.

$y=2x\{y\}=2\{x\}$

The line through $P_1\{P\}\_1$ and $P_2\{P\}\_2$ passes through the origin, since for $x=0x=0$ the $yy$-value is equal to 0.

Insert the two points into the general line equation:

$y=mx+ty=mx+t$

$\begin{array}{c}1)3.5=-1m+t\\ 2)-2=2m+t\end{array}\backslash def\backslash arraystretch\{1.25\}\; \backslash begin\{array\}\{l\}1)\backslash ;3.5=-1m+\; t\backslash \backslash 2)\backslash ;-2=2\; m+\; t\backslash end\{array\}$

For example, solve the linear system of equations with the addition method.

First multiply equation $11$) on both sides by $\mathrm{\mid }\cdot (-1)|\backslash cdot\; (-1)$

$\begin{array}{c}1)-3.5=m-t\\ 2)-2=2m+t\end{array}\backslash def\backslash arraystretch\{1.25\}\; \backslash begin\{array\}\{l\}1)\backslash ;-3.5=\; m\; -\; t\backslash \backslash 2)\backslash ;-2=2m\; +\; t\backslash end\{array\}$

Compute $1)+2)1)\; +\; 2)$

Plug $mm$ into one of the two equations.

Plug $mm$ and $tt$ into the general line equation.

$m=-\frac{11}{6};t=\frac{5}{3}m=-\backslash frac\{11\}\{6\};t=\backslash frac\{5\}\{3\}$

$y=-\frac{11}{6}\cdot x+\frac{5}{3}y=-\backslash frac\{11\}\{6\}\backslash cdot\; x+\backslash frac\{5\}\{3\}$

The line through $P_1\{P\}\_1$ and $P_2\{P\}\_2$ does not pass through the origin, because for $x=0x=0$ the $yy$-value is equal to ${\displaystyle \frac{5}{3}}\backslash dfrac\{5\}\{3\}$.