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Algebra / Linear equations in two variables Difficulty: Medium

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

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?

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Explanation

Choice A is correct. The slope, $m$ , of a line in the xy-plane can be found using two points on the line, $left parenthesis x 1 comma y 1 right parenthesis$ and $left parenthesis x 2 comma y 2 right parenthesis$ , and the slope formula $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ . 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 $left parenthesis 0 comma n right parenthesis$ , where $n$ is a constant. Substituting two of these points, $(- 3, n + 92)$ and $left parenthesis 0 comma n right parenthesis$ , for $left parenthesis x 1 comma y 1 right parenthesis$ and $left parenthesis x 2 comma y 2 right parenthesis$ , respectively, in the slope formula yields $m = \frac{n - (n + 92)}{0 - (- 3)}$ , which is equivalent to $m = \frac{n - n - 92}{0 + 3}$ , or $m = - \frac{92}{3}$ . Therefore, the slope of the line that represents this relationship in the xy-plane is $- \frac{92}{3}$ .

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.