x y 0 18 1 13 2 8 The table shows three values of x and their corresponding values of

Question

x y 0 18 1 13 2 8 The table shows three values of x and their corresponding values of y . There is a linear relationship between x and y . Which of the following equations represents this relationship?

Accepted Answer

Choice D is correct. A linear relationship can be represented by an equation of the form y = m x + b , where m and b are constants. It&rsquo;s given in the table that when x = 0 , y = 18 . Substituting 0 for x and 18 for y in y = m x + b yields 18 = m 0 + b , or 18 = b . Substituting 18 for b in the equation y = m x + b yields y = m x + 18 . It&rsquo;s also given in the table that when x = 1 , y = 13 . Substituting 1 for x and 13 for y in the equation y = m x + 18 yields 13 = m 1 + 18 , or 13 = m + 18 . Subtracting 18 from both sides of this equation yields - 5 = m . Therefore, the equation y = - 5 x + 18 represents the relationship between x and y . 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.

$x$	$y$
$0$	$18$
$1$	$13$
$2$	$8$

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