x y - 6 n + 184 - 3 n + 92 0 n The table shows three values of

Question

x y - 6 n + 184 - 3 n + 92 0 n The table shows three values of x and their corresponding values of y , where n is a constant, for the linear relationship between x and y . What is the slope of the line that represents this relationship in the xy -plane?

Accepted Answer

Choice A is correct. The slope, m , of a line in the xy -plane can be found using 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 . Based on the given table, the line representing the relationship between x and y in the xy -plane passes through the points - 6 , n + 184 , - 3 , n + 92 , and 0 , n , where n is a constant. Substituting two of these points, - 3 , n + 92 and 0 , n , for x 1 , y 1 and x 2 , y 2 , respectively, in the slope formula yields m = n - n + 92 0 - - 3 , which is equivalent to m = n - n - 92 0 + 3 , or m = - 92 3 . Therefore, the slope of the line that represents this relationship in the xy -plane is - 92 3 . Choice B is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

$x$	$y$
$negative 6$	$n plus 184$
$negative 3$	$n plus 92$
$0$	$n$

Question x-y-6-