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At how many points do the graphs of the equations $y=x+20$ and $y=8x$ intersect in the $xy$-plane?

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At how many points do the graphs of the equations $y=x+20$ and $y=8x$ intersect in the $xy$-plane?

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Choice B is correct. Each given equation is written in slope-intercept form, $y=mx+b$, where $m$ is the slope and $(0,b)$ 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.

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At how many points do the graphs of the equations $y=x+20$ and $y=8x$ intersect in the $xy$-plane?

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