Question 6 (1 point) The graph of 9x-10y=19 is translated down 4 units in the xy-plane . What is the x <coordinate of the x-intercept t of the resulting graph? __ (enter fraction, use/for fraction) Blank 1: square

To find the x-coordinate of the x-intercept of the resulting graph after translating the graph of $9x-10y=19$ down 4 units, we need to follow these steps:<br /><br />1. Find the equation of the translated graph.<br />2. Find the x-intercept of the translated graph.<br /><br />Step 1: Find the equation of the translated graph.<br />The equation of the translated graph can be found by subtracting 4 from the y-coordinate of every point on the original graph. This is because translating a graph down or up involves changing the y-coordinates of the points while keeping the x-coordinates the same.<br /><br />The equation of the original graph is $9x-10y=19$. To translate this down 4 units, we subtract 4 from the y-coordinate in the equation. This gives us the equation of the translated graph:<br /><br />$9x-10(y-4)=19$<br /><br />Simplifying this equation, we get:<br /><br />$9x-10y+40=19$<br /><br />Step 2: Find the x-intercept of the translated graph.<br />To find the x-intercept, we set y = 0 in the equation and solve for x:<br /><br />$9x-10(0)+40=19$<br /><br />Simplifying this equation, we get:<br /><br />$9x+40=19$<br /><br />Subtracting 40 from both sides, we get:<br /><br />$9x=-21$<br /><br />Dividing both sides by 9, we get:<br /><br />$x=-\frac{21}{9}$<br /><br />Simplifying the fraction, we get:<br /><br />$x=-\frac{7}{3}$<br /><br />Therefore, the x-coordinate of the x-intercept of the resulting graph is $-\frac{7}{3}$.