Find the equation of the straight line which cuts off an intercept $2$ from the positive direction of the $Y$ axis and is inclined at $45^\circ$ to the positive direction of the $X$ axis.
Intercept from the positive direction of the $Y$ axis $= c = 2$
Inclination of the required line to the positive direction of the $X$ axis $= \theta = 45^\circ$
$\therefore \;$ Slope of the required line $= m = \tan \theta = 1$
The equation of the required line is of the form: $\;$ $y = mx + c$
i.e. $\;$ $y = 1 \times x + 2$
$\therefore \;$ The equation of the required line is: $\;$ $y = x + 2$