In the xy -plane, line k passes through the points 0 , - 5 and 1 , - 1 .

Question

In the xy -plane, line k passes through the points 0 , - 5 and 1 , - 1 . Which equation defines line k ?

Accepted Answer

Choice D is correct. An equation defining a line in the xy -plane can be written in the form y = m x + b , where m represents the slope and 0 , b represents the y -intercept of the line. It&rsquo;s given that line k passes through the point 0 , - 5 ; therefore, b = - 5 . The slope, m , of a line can be found using any two points on the line, x 1 , y 1 and x 2 , y 2 , and the slope formula m = y 2 - y 1 x 2 - x 1 . Substituting the points 0 , - 5 and 1 , - 1 for x 1 , y 1 and x 2 , y 2 , respectively, in the slope formula yields m = - 1 - - 5 1 - 0 , or m = 4 . Substituting 4 for m and - 5 for b in the equation y = m x + b yields y = 4 x - 5 . Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors.

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