The graph of 7 x + 2 y = - 31 in the x y -plane has an x -intercept

Question

The graph of 7 x + 2 y = - 31 in the x y -plane has an x -intercept at ( a , 0 ) and a y -intercept at ( 0 , b ) , where a and b are constants. What is the value of b a ?

Accepted Answer

Choice D is correct. The x -coordinate a of the x -intercept a , 0 can be found by substituting 0 for y in the given equation, which gives 7 x + 2 0 = - 31 , or 7 x = - 31 . Dividing both sides of this equation by 7 yields x = - 31 7 . Therefore, the value of a is - 31 7 . The y -coordinate b of the y -intercept 0 , b can be found by substituting 0 for x in the given equation, which gives 7 0 + 2 y = - 31 , or 2 y = - 31 . Dividing both sides of this equation by 2 yields y = - 31 2 . Therefore, the value of b is - 31 2 . It follows that the value of b a is - 31 2 - 31 7 , which is equivalent to 31 2 7 31 , or 7 2 . 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.

Question the-gr