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x y −2s 24 −s 21 s 15 The table shows three values of x and their corresponding values of y, where s is a constant. There is a linear relationship between x and y. Which of the following equations represents this relationship? +3 = 18
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice B is correct. The linear relationship between x and y can be represented - = - by an equation of the form y y1 m^x x1h, where m is the slope of the graph of , 1 1 the equation in the xy-plane and ^x yh is a point on the graph. The = s y lo 2- pe y 1 of a line can be found using two points on the line and the slope formula m x2- x 1. Each value of x and its corresponding value of y in the table can be represented by a - ,21 ,15 1 , 1 2 , 2 point ^x,yh. Substituting the points ^ s h and ^s h for ^x yh and ^x yh, = 15-21 =-6 respectively, in the slope formula yields m -- , which gives m 2 , or =-3 -3 s ^,1 sh5 1 , 1 s m . Substituting for m and the point ^s h for ^x yh in the equation - = s - s -15=- 3 - -3 y y1 m^x x1h yields y ^x sh. Distributing on the right-hand -15= s - 3 x+3 15 s side of this equation yields y . Adding to each side of this =- 3 x+18 s equation yields y . Multiplying each side of this equation by s yields s =-3 +18 3 + =18 sy x s. Adding 3x to each side of this equation yields x sy s. 3 + =18 Therefore, the equation x sy s represents this relationship. Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors. 37 SAT PRACTICE TEST #7 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1
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