Choice B is correct. A line in the xy-plane with a slope of $m$ and a y-intercept of $left parenthesis 0 comma b right parenthesis$ can be represented by the equation $y = m x + b$ . It's given that the line has a slope of $- \frac{1}{2}$ . Therefore, $m = - \frac{1}{2}$ . It's also given that the line passes through the point $left parenthesis 0 comma 3 right parenthesis$ . Therefore, $b equals 3$ . Substituting $- \frac{1}{2}$ for $m$ and $3$ for $b$ in the equation $y = m x + b$ yields $y = - \frac{1}{2} x + 3$ . Therefore, the equation $y = - \frac{1}{2} x + 3$ represents this line.

Choice A is incorrect. This equation represents a line in the xy-plane that passes through the point $left parenthesis 0 comma negative 3 right parenthesis$ , not $left parenthesis 0 comma 3 right parenthesis$ .

Choice C is incorrect. This equation represents a line in the xy-plane that has a slope of $\frac{1}{2}$ , not $- \frac{1}{2}$ , and passes through the point $left parenthesis 0 comma negative 3 right parenthesis$ , not $left parenthesis 0 comma 3 right parenthesis$ .

Choice D is incorrect. This equation represents a line in the xy-plane that has a slope of $\frac{1}{2}$ , not $- \frac{1}{2}$ .