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The slopes of the lines, making angle of measures $45^{\circ}$ with the line $2 x-3 y=5$ are
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$5, \frac{-1}{5}$
Let the required slope of the line be $m$
$\begin{aligned} & \Rightarrow \tan 45^{\circ}=\left|\frac{m-\frac{2}{3}}{1+m \times \frac{2}{3}}\right| \\ & \Rightarrow \frac{3 m-2}{3+2 m}= \pm 1 \\ & \Rightarrow m=5 \text { or } m=\frac{-1}{5}\end{aligned}$
$\begin{aligned} & \Rightarrow \tan 45^{\circ}=\left|\frac{m-\frac{2}{3}}{1+m \times \frac{2}{3}}\right| \\ & \Rightarrow \frac{3 m-2}{3+2 m}= \pm 1 \\ & \Rightarrow m=5 \text { or } m=\frac{-1}{5}\end{aligned}$
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