At how many points do the graphs of the equations y = x + 20 and

Choice B is correct. Each given equation is written in slope-intercept form, $y=mx+b$, where $m$ is the slope and $\left(0,b\right)$ is the y-intercept of the graph of the equation in the xy-plane. The graphs of two lines that have different slopes will intersect at exactly one point. The graph of the first equation is a line with slope $1$. The graph of the second equation is a line with slope $8$. Since the graphs are lines with different slopes, they will intersect at exactly one point.

Choice A is incorrect because two graphs of linear equations have $0$ intersection points only if they are parallel and therefore have the same slope.

Choice C is incorrect because two graphs of linear equations in the xy-plane can have only $0$, $1$, or infinitely many points of intersection.

Choice D is incorrect because two graphs of linear equations in the xy-plane can have only $0$, $1$, or infinitely many points of intersection.