Exercises: Linear functions and line equations

Insert the two points into the general line equation:

$y=mx+t$

$\begin{array}{rlll}1)& 4& =& 2\mathrm{m}+\mathrm{t}\\ 2)& -3& =& -1.5\mathrm{m}+\mathrm{t}& |\cdot (-1)\end{array}$

$\begin{array}{rllll}1)& 4& =& 2\mathrm{m}+\mathrm{t}& \\ 2)& 3& =& 1.5\mathrm{m}-\mathrm{t}& \end{array}$

Use the addition method.

Compute $1)+2)$.

Plug $m$ into one of the two functions.

$y=2x$

The line through $P_1$ and $P_2$ passes through the origin, since for $x=0$ the $y$-value is equal to 0.

Insert the two points into the general line equation:

$y=mx+t$

$\begin{array}{l}1)3.5=-1m+t\\ 2)-2=2m+t\end{array}$

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

First multiply equation $1$) on both sides by $|\cdot (-1)$

$\begin{array}{l}1)-3.5=m-t\\ 2)-2=2m+t\end{array}$

Compute $1)+2)$

Plug $m$ into one of the two equations.

Plug $m$ and $t$ into the general line equation.

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

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

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