The relationship between two variables, x and y , is linear. For every increase in the value of x by

Question

The relationship between two variables, $x$ and $y$ , is linear. For every increase in the value of $x$ by $1$ , the value of $y$ increases by $8$ . When the value of $x$ is $2$ , the value of $y$ is $18$ . Which equation represents this relationship?

A.

$y = 8 x + 2$

B.

$y = 2 x + 18$

C.

$y = 2 x + 8$

D.

$y = 3 x + 26$

Accepted Answer

Choice C is correct. It&rsquo;s given that the relationship between x and y is linear. An equation representing a linear relationship can be written in the form y = m x + b , where m is the slope and b is the y -coordinate of the y -intercept of the graph of the relationship in the xy -plane. It&rsquo;s given that for every increase in the value of x by 1 , the value of y increases by 8 . The slope of a line can be expressed as the change in y over the change in x . Thus, the slope, m , of the line representing this relationship can be expressed as 8 1 , or 8 . Substituting 8 for m in the equation y = m x + b yields y = 8 x + b . It's also given that when the value of x is 2 , the value of y is 18 . Substituting 2 for x and 18 for y in the equation y = 8 x + b yields 18 = 8 2 + b , or 18 = 16 + b . Subtracting 16 from each side of this equation yields 2 = b . Substituting 2 for b in the equation y = 8 x + b yields y = 8 x + 2 . Therefore, the equation y = 8 x + 2 represents this relationship. Choice A is incorrect. This equation represents a relationship where for every increase in the value of x by 1 , the value of y increases by 2 , not 8 , and when the value of x is 2 , the value of y is 22 , not 18 . Choice B is incorrect. This equation represents a relationship where for every increase in the value of x by 1 , the value of y increases by 2 , not 8 , and when the value of x is 2 , the value of y is 12 , not 18 . Choice D is incorrect. This equation represents a relationship where for every increase in the value of x by 1 , the value of y increases by 3 , not 8 , and when the value of x is 2 , the value of y is 32 , not 18 .

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