Determine the point on the graph of the linear equation 2x+ 5y = 19

Let $x$ be the abscissa of the given line $2 x+5 y=19$, then by given condition,

Ordinate $(y)=1 \frac{1}{2} \times$ Abscissa

$\Rightarrow$   $y=\frac{3}{2} x$  $\ldots$ (i)

On putting $y=\frac{3}{2} x$ in given equation, we get

$2 x+5\left(\frac{3}{2}\right) x=19$

$\Rightarrow \quad 4 x+15 x=19 \times 2$

$\Rightarrow \quad 4 x+15 x=38$

$\Rightarrow \quad 19 x=38$

$\Rightarrow \quad x=\frac{38}{19}$

$\therefore \quad x=2$

On substituting the value of $x$ in Eq. (0), we get

$y=\frac{3}{2} \times 2=3$

$\Rightarrow \quad y=3$

Hence, the required point is $(2,3)$.