Linear Equations - Forms of a Line

$A = (18,0), B = (0,9)$ $\phantom{0}$ $\begin{aligned}\overline{AB}^2 &= 18^2 + 9^2 \\ &= (2\cdot9)^2 + 9^2 \\ &= (5)(9^2) \\ \\ \overline{AB} &= \sqrt{(5)(9^2)} \\ &= \boxed{9 \sqrt{5}} \end{aligned}$

The line intersects the $x$ -axis when $y=0.$ Substituting $y=0,$ we have $x+2 \cdot 0=18 \Rightarrow x=18.$ Hence, $A=(18,0).$

The line intersects the $y$ -axis when $x=0.$ Substituting $x=0,$ we have $0+2y=18 \Rightarrow y=9.$ Hence, $B=(0,9)$ .

Thus, the length of the line segment $AB$ is $\overline{AB}=\sqrt{{18}^2+{9}^2} = 9\sqrt{5}.$