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Algebra / Systems of two linear equations in two variables Difficulty: Medium

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

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Explanation

Choice B is correct. Each given equation is written in slope-intercept form, $y = m x + b$ , where $m$ is the slope and $left parenthesis 0 comma b right parenthesis$ 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.