At how many points do the graphs of the equations y = x + 20 and y = 8 x

Question

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

Accepted Answer

Choice B is correct. Each given equation is written in slope-intercept form, y = m x + 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.

Question 07807e