Further exercises: Linear functions

Consider the set of points $P(\frac{k}{2}\cdot \sqrt{2}|k)$ for different $k$.

To find the general equation of a straight line, we need two points on the straight line.

Therefore, it is best to choose here e.g. the two points $F(\frac{k}{2}\cdot \sqrt{2}|k)$and $G(\frac{k+1}{2}\cdot \sqrt{2}|k+1)$.

y$=m\cdot x+t$

First determine the slope $m$.

$${\displaystyle m=\frac{k+1-k}{\frac{k+1}{2}\cdot \sqrt{2}-\frac{k}{2}\cdot \sqrt{2}}=\frac{1}{\frac{\sqrt{2}}{2}}=\frac{2}{\sqrt{2}}}$$

Now you can insert $m$ and one of the points, e.g. $P$, into the general line equation.

$k=\underset{=k}{\underbrace{\frac{k}{2}\cdot \sqrt{2}\cdot \frac{2}{\sqrt{2}}}}+t$

Solve for $t$.

$\Rightarrow$ t=0

Wrtite down the equation of the straight line.

$y=\frac{2}{\sqrt{2}}\cdot x$