If the x-intercept of the line $\mathrm{y}=\mathrm{mx}+2$ is greater than 1 /2, then the gradient of the line lies in the interval  

Given equation of line is $\mathrm{y}=\mathrm{mx}+2$

$\Rightarrow \frac{\mathrm{x}}{-\frac{2}{\mathrm{m}}}+\frac{\mathrm{y}}{2}=1$

it is given that x-intercept of the above line is greater than $\frac{1}{2}$

$\therefore -\frac{2}{\mathrm{m}}-\frac{1}{2}>0$

$\Rightarrow -\frac{2}{\mathrm{m}}-\frac{1}{2}>0$

$\Rightarrow -\left(\frac{4+\mathrm{m}}{2\mathrm{m}}\right)>0$

$\Rightarrow \frac{4+\mathrm{m}}{2\mathrm{m}}<0$

$\Rightarrow -4<\mathrm{m}<0$