Further exercises: Linear functions

Show that the line $g$ through $P_{1} (\sqrt{k} / k)$ and $P_{2} (1 / 1)$ has the slope $a_{1} = \sqrt{k} + 1$ and intersects the y-axis at $P_{y} (0 / - \sqrt{k})$

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$k - 1$	$=$	$ m \sqrt{k} - m + t - t$
	↓	conclude
$k - 1$	$=$	$m (\sqrt{k} - 1)$
	↓	solve for $m$
$m$	$=$	$\frac{k - 1}{\sqrt{k} - 1}$
	↓	simplify using the binomial theorems ( $k = {\sqrt{k}}^{2})$ .
$m$	$=$	$\frac{(\sqrt{k} + 1) (\sqrt{k} - 1)}{\sqrt{k} - 1}$
$m$	$=$	$\sqrt{k} + 1$
	↓	use 2)
$1$	$=$	$(\sqrt{k} + 1) \cdot 1 + t$
	↓	solve for $t$
$t$	$=$	$1 - (\sqrt{k} + 1)$
$t$	$=$	$- \sqrt{k}$