If the straight line, $2\mathrm{x}-3\mathrm{y}+17=0$ is perpendicular to the line passing through the points (7,17) and (15,$\mathrm{\beta }$), then $\mathrm{\beta }$=

 Slope of $2\mathrm{x}-3\mathrm{y}+17=0\text{ is }2/3$
Slope of line joining $(7,17),(15,\mathrm{\beta }) \mathrm{is} \frac{\mathrm{\beta }-17}{15-7}=\frac{\mathrm{\beta }-17}{8}.$
The lines are perpendicular $\Rightarrow \left(\frac{2}{3}\right)\left(\frac{\mathrm{\beta }-17}{8}\right)=-1\Rightarrow \mathrm{\beta }-17=-12\Rightarrow \mathrm{\beta }=5$