x y - 2 s 24 - s 21 s 15 The table shows three values of x and their

Question

x y - 2 s 24 - s 21 s 15 The table shows three values of x and their corresponding values of y , where s is a constant. There is a linear relationship between x and y . Which of the following equations represents this relationship?

Accepted Answer

Choice B is correct. The linear relationship between x and y can be represented by an equation of the form y - y 1 = m x - x 1 , where m is the slope of the graph of the equation in the xy -plane and x 1 , y 1 is a point on the graph. The slope of a line can be found using two points on the line and the slope formula m = y 2 - y 1 x 2 - x 1 . Each value of x and its corresponding value of y in the table can be represented by a point x , y . Substituting the points - s , 21 and s , 15 for x 1 , y 1 and x 2 , y 2 , respectively, in the slope formula yields m = 15 - 21 s - - s , which gives m = - 6 2 s , or m = - 3 s . Substituting - 3 s for m and the point s , 15 for x 1 , y 1 in the equation y - y 1 = m x - x 1 yields y - 15 = - 3 s x - s . Distributing - 3 s on the right-hand side of this equation yields y - 15 = - 3 x s + 3 . Adding 15 to each side of this equation yields y = - 3 x s + 18 . Multiplying each side of this equation by s yields s y = - 3 x + 18 s . Adding 3 x to each side of this equation yields 3 x + s y = 18 s . Therefore, the equation 3 x + s y = 18 s represents this relationship. Choice A 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.

$x$	$y$
$minus 2 s$	$24$
$- s$	$21$
$s$	$15$

Question x-y-2-