OG详解-OG4 数学1 Q15

Choice D is correct. The equation that defines line t in the xy-plane can be written in slope-intercept form y = mx + b, where m is the slope of line t and (0, b) is its y-intercept. It’s given that line t has a slope of - 1​3​. Therefore, m =- 1​3​     .Substituting - 1​3​for m in the equation y = mx + b yields y =- 1​3​x + b, ory =- x​3​ + b. It’s also given that line t passes through the point (9, 10).Substituting 9 for x and 10 for y in the equation y =- x​3​+ b yields10 =- 9​3​+ b , or 10 =-3 + b. Adding 3 to both sides of this equation yields13=b. Substituting 13 for b in the equation y =- x​3​  + b yields y =- x​3​+13.Choice A is incorrect and may result from conceptual or calculation errors.Choice B is incorrect. This equation defines a line that has a slope of 9, not -1​3​,and passes through the point (0, 10), not (9, 10). Choice C is incorrect. This equation defines a line that passes through the point (0, 10), not (9, 10).