OG详解-OG1 数学1 Q24

Choice D is correct. The equation of line  h  can be written in slope-intercept form y = mx + b, where m  is the slope of the line and (0,b) is they-intercept of the line. It’s given that line  h  contains the points  (18,130),  (23,160), and  (26,178).Therefore, its slope  m  can be found as160−13023−18​​ , or  6. Substituting 6  for  m  in the equation y = mx + b yields y = 6x + b. Substituting 130 for y  and 18  for x in this equation yields 130 = 6 (18)+ b, or 130 = 108 + b. Subtracting 108  from both sides of this equation yields 22 = b. Substituting 22 for b in y = 6x + b yields y = 6x +22 . Since line k  is the result of translating line  h  down 5  units, an equation of line k  is y = 6x +22-5, or y = 6x +17. Substituting 0  for y  in this equation yields 0 = 6x +17. Solving this equation for x  yields x = -176​​ . Therefore, the x-intercept of line  k  is (- 176,0).
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 error.