A line in the xy -plane has a slope of - 1 2 and passes through the point 0 ,

Question

A line in the xy -plane has a slope of - 1 2 and passes through the point 0 , 3 . Which equation represents this line?

Accepted Answer

Choice B is correct. A line in the xy -plane with a slope of m and a y -intercept of 0 , b can be represented by the equation y = m x + b . It's given that the line has a slope of - 1 2 . Therefore, m = - 1 2 . It's also given that the line passes through the point 0 , 3 . Therefore, b = 3 . Substituting - 1 2 for m and 3 for b in the equation y = m x + b yields y = - 1 2 x + 3 . Therefore, the equation y = - 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 0 , - 3 , not 0 , 3 . Choice C is incorrect. This equation represents a line in the xy -plane that has a slope of 1 2 , not - 1 2 , and passes through the point 0 , - 3 , not 0 , 3 . Choice D is incorrect. This equation represents a line in the xy -plane that has a slope of 1 2 , not - 1 2 .

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