x y - 18 - 48 7 52 The table shows two values of x and their corresponding values of

Question

x y - 18 - 48 7 52 The table shows two values of x and their corresponding values of y . In the xy -plane, the graph of the linear equation representing this relationship passes through the point 1 7 , a . What is the value of a ?

Accepted Answer

Choice D is correct. The linear relationship between x and y can be represented by the equation y = m x + b , where m is the slope of the graph of this equation in the xy -plane and b is the y -coordinate of the y -intercept. The slope of a line between any two points x 1 , y 1 and x 2 , y 2 on the line can be calculated using the slope formula m = y 2 - y 1 x 2 - x 1 . Based on the table, the graph contains the points - 18 , - 48 and 7 , 52 . Substituting - 18 , - 48 and 7 , 52 for x 1 , y 1 and x 2 , y 2 , respectively, in the slope formula yields m = 52 - - 48 7 - - 18 , which is equivalent to m = 100 25 , or m = 4 . Substituting 4 for m , - 18 for x , and - 48 for y in the equation y = m x + b yields - 48 = 4 - 18 + b , or - 48 = - 72 + b . Adding 72 to both sides of this equation yields 24 = b . Therefore, m = 4 and b = 24 . Substituting 4 for m and 24 for b in the equation y = m x + b yields y = 4 x + 24 . Thus, the equation y = 4 x + 24 represents the linear relationship between x and y . It's also given that the graph of the linear equation representing this relationship in the xy -plane passes through the point 1 7 , a . Substituting 1 7 for x and a for y in the equation y = 4 x + 24 yields a = 4 1 7 + 24 , which is equivalent to a = 4 7 + 168 7 , or a = 172 7 . 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.

$x$	$y$
$negative 18$	$negative 48$
$7$	$52$

Question x-y-18