Question: Find the ordered pair of the point that lies at $x = \frac{8}{17}$, given the function below:
$f(x) = -6x - 1$
1. **State the problem:** We need to find the ordered pair $(x, y)$ on the graph of the function $f(x) = -6x - 1$ when $x = \frac{8}{17}$.
2. **Formula used:** The function is given by $f(x) = -6x - 1$. To find the $y$-coordinate for a given $x$, substitute $x$ into the function.
3. **Substitute $x = \frac{8}{17}$:**
$$
y = f\left(\frac{8}{17}\right) = -6 \times \frac{8}{17} - 1
$$
4. **Multiply:**
$$
y = -\frac{48}{17} - 1
$$
5. **Convert $1$ to fraction with denominator $17$:**
$$
y = -\frac{48}{17} - \frac{17}{17}
$$
6. **Combine fractions:**
$$
y = -\frac{48 + 17}{17} = -\frac{65}{17}
$$
7. **Final ordered pair:**
$$
\left(\frac{8}{17}, -\frac{65}{17}\right)
$$
**Answer:** The ordered pair is $\left(\frac{8}{17}, -\frac{65}{17}\right)$.