OG详解-OG6 数学1 Q16

Choice C is correct. It’s given that the relationship between x and y is linear. An equation representing a linear relationship can be written in the form y = mx+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’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  81​​, or 8. Substituting 8 for m in the equation y = mx+b yields y = 8x+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 = 8x+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 = 8x+b yields y = 8x+2. Therefore, the equation y = 8x+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.