To solve the problem, we need to determine the new equation of the graph after it has been translated down 4 units and then find the x-coordinate of the x-intercept of the new graph.
1. Translate the graph down 4 units:
- The original equation of the graph is [tex]\(9x - 10y = 19\)[/tex].
- Translating a graph down 4 units effectively means reducing the y-value of each point on the graph by 4. However, we can achieve the same effect by adjusting the constant term in the equation:
[tex]\[
9x - 10(y + 4) = 19
\][/tex]
- Simplify the equation:
[tex]\[
9x - 10y - 40 = 19
\][/tex]
- Solve for the new equation:
[tex]\[
9x - 10y = 59
\][/tex]
2. Find the x-intercept of the translated graph:
- The x-intercept occurs where [tex]\(y = 0\)[/tex].
- Substitute [tex]\(y = 0\)[/tex] into the new equation:
[tex]\[
9x - 10(0) = 59
\][/tex]
- Simplify:
[tex]\[
9x = 59
\][/tex]
- Solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{59}{9}
\][/tex]
3. Final result:
- The x-coordinate of the x-intercept of the translated graph is:
[tex]\[
x \approx 6.555555555555555
\][/tex]
Thus, the x-coordinate of the x-intercept of the resulting graph is approximately [tex]\(6.56\)[/tex].
