x 1 2 3 y 11 16 21 The table shows three values of x and their corresponding values of

Question

x 1 2 3 y 11 16 21 The table shows three values of x and their corresponding values of y . Which equation represents the linear relationship between x and y ?

Accepted Answer

Choice A 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 line in the xy -plane that represents the relationship, and b is the y -coordinate of the y -intercept. The slope can be computed using any two points on the line. 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 . In the given table, each value of x and its corresponding value of y can be represented by a point x , y . In the given table, when the value of x is 1 , the corresponding value of y is 11 and when the value of x is 2 , the corresponding value of y is 16 . Therefore, the points 1 , 11 and 2 , 16 are on the line. Substituting 1 , 11 and 2 , 16 for x 1 , y 1 and x 2 , y 2 , respectively, in the slope formula yields m = 16 - 11 2 - 1 , or m = 5 . Substituting 5 for m in the equation y = m x + b yields y = 5 x + b . Substituting the first value of x in the table, 1 , and its corresponding value of y , 11 , for x and y , respectively, in this equation yields 11 = 5 1 + b , or 11 = b + 5 . Subtracting 5 from both sides of this equation yields 6 = b . Substituting 6 for b in the equation y = 5 x + b yields y = 5 x + 6 . Therefore, the equation y = 5 x + 6 represents the linear relationship between x and y . Choice B is incorrect. For this relationship, when the value of x is 1 , the corresponding value of y is 16 , not 11 . Choice C is incorrect. For this relationship, when the value of x is 2 , the corresponding value of y is 17 , not 16 . Choice D is incorrect. For this relationship, when the value of x is 1 , the corresponding value of y is 17 , not 11 .

$x$	$1$	$2$	$3$
$y$	$11$	$16$	$21$

Question x-1-2-