OG详解-OG7 数学1 Q44

Choice B is correct. The linear relationship between x and y can be represented by an equation of the form y-y₁ = m(x-x₁), where m is the slope of the graph of the equation in the xy-plane and (x₁, y₁) is a point on the graph. The slope of a line can be found using two points on the line and the slope formula m = y₂−y₁x₂−x₁. Each value of x and its corresponding value of y in the table can be represented by a point (x, y). Substituting the points (-s, 21) and (s, 15) for (x₁, y₁) and (x₂, y₂), respectively, in they₂−y₁x₂−x_1​​ slope formula yields m = 15−21s−(−s​)​ , which gives m = −62s​​ or m=−​3s​. Substituting -​3s​ for m and the point (s,15)  for (x₁, y₁) in the equation y-y₁ = m(x-x₁) yields y-15 = - ​3s​ (x-s). Distributing −​3s​  on the right-hand  side of this equation yields y- 15 = -​3xs​+3. Adding 15 to each side of this equation yields y = -​3xs​ + 18. Multiplying each side of this equation by s yields sy =-3x+18s. Adding 3x to each side of this equation yields 3x+sy = 18s. Therefore, the equation 3x+sy = 18s 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.