The graph of 9 x - 10 y = 19 is translated down 4 units in the xy -plane. What

Question

The graph of 9 x - 10 y = 19 is translated down 4 units in the xy -plane. What is the x -coordinate of the x -intercept of the resulting graph?

Accepted Answer

The correct answer is 59 9 . When the graph of an equation in the form A x + B y = 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 A x + B y + k = C . It&rsquo;s given that the graph of 9 x - 10 y = 19 is translated down 4 units in the xy -plane. Therefore, the resulting graph can be represented by the equation 9 x - 10 y + 4 = 19 , or 9 x - 10 y - 40 = 19 . Adding 40 to both sides of this equation yields 9 x - 10 y = 59 . The x -coordinate of the x -intercept of the graph of an equation in the xy -plane is the value of x in the equation when y = 0 . Substituting 0 for y in the equation 9 x - 10 y = 59 yields 9 x - 10 0 = 59 , or 9 x = 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.

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