Short Answer 
To find the x-intercept of the original line equation (9x – 10y = 19), set (y) to 0, resulting in an x-intercept of (19/9). After translating the line down by 4 units, the new equation becomes (9x – 10y = 59), giving a new x-intercept of (59/9).
Step 1: Understand the Original Equation
The original equation of the line is given as 9x – 10y = 19. To find the x-intercept, set y to 0. Rearranging this equation leads to the expression x = (19 + 10y) / 9. Plugging y = 0 into this equation results in the original x-intercept of 19/9.
Step 2: Translate the Line Downward
To translate the line down by 4 units, modify the equation by decreasing the y values. This can be achieved by adjusting the constant term in the equation: 9x – 10y = 19 becomes 9x – 10y = 19 + (10 ‚à öo 4). Thus, the new equation for the translated line is 9x – 10y = 59.
Step 3: Determine the New X-Intercept
To find the x-intercept of the new equation 9x – 10y = 59, again set y to 0. This leads to the equation transforming to x = (59 + 10y) / 9. Setting y = 0 yields a new x-intercept of 59/9.