For the linear function g , the graph of y = g ( x ) in the xy -plane has

Question

For the linear function g , the graph of y = g ( x ) in the xy -plane has a slope of 2 and passes through the point 1 , 14 . Which equation defines g ?

Accepted Answer

Choice C is correct. An equation defining a linear function can be written in the form g x = m x + b , where m is the slope and 0 , b is the y -intercept of the graph of y = g x in the xy -plane. It&rsquo;s given that the graph of y = g x has a slope of 2 . Therefore, m = 2 . It&rsquo;s also given that the graph of y = g x passes through the point 1 , 14 . It follows that when x = 1 , g x = 14 . Substituting 1 for x , 14 for g x , and 2 for m in the equation g x = m x + b yields 14 = 2 1 + b , or 14 = 2 + b . Subtracting 2 from each side of this equation yields 12 = b . Therefore, b = 12 . Substituting 2 for m and 12 for b in the equation g x = m x + b yields g x = 2 x + 12 . Therefore, the equation that defines g is g x = 2 x + 12 . Choice A is incorrect. For this function, the graph of y = g x in the xy -plane passes through the point 1 , 2 , not 1 , 14 . Choice B is incorrect. For this function, the graph of y = g x in the xy -plane passes through the point 1 , 4 , not 1 , 14 . Choice D is incorrect. For this function, the graph of y = g x in the xy -plane passes through the point 1 , 16 , not 1 , 14 .

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