OG详解-OG3 数学2 Q21

The correct answer is 59​9​. When the graph of an equation in the form  Ax +By = C, where A, B , and C are constants, is translated down k units in the xy-plane, the resulting graph can be represented by the equation Ax +B (y+k)= C. It’s given that the graph of 9x -10y = 19 is translated down 4 units in the xy-plane. Therefore, the resulting graph can be represented by the equation 9x -10 (y+4)= 19, or 9x -10y - 40 = 19. Adding 40 to both sides of this equation yields 9x -10y = 59. The x-coordinate of the x-intercept of the graph of an equation in the xy-plane is the value of x the equation when y = 0. Substituting 0 for y in the equation 9x -10y = 59 yields 9x -10(0)= 59, or 9x = 59. Dividing both sides of this equation by 9 yields x =59​9​. Therefore, the  x-coordinate of the x-intercept of the resulting graph is 59​9​. Note that 59/9, 6.555, and 6.556 are examples of ways to enter a correct answer.