Question: Find the ordered pair of the point that lies at $x = \frac{8}{17}$, given the function below:
$f(x) = -6x - 1$
Graph shape: linear function (a straight line) with equation $f(x) = -6x - 1$, position_hint = center
1. **State the problem:** We need to find the ordered pair $(x, y)$ on the line defined by 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 $x = \frac{8}{17}$:**
$$f\left(\frac{8}{17}\right) = -6 \times \frac{8}{17} - 1$$
4. **Multiply:**
$$-6 \times \frac{8}{17} = \frac{-48}{17}$$
5. **Rewrite the expression:**
$$f\left(\frac{8}{17}\right) = \frac{-48}{17} - 1$$
6. **Convert $1$ to fraction with denominator $17$:**
$$1 = \frac{17}{17}$$
7. **Subtract fractions:**
$$\frac{-48}{17} - \frac{17}{17} = \frac{-48 - 17}{17} = \frac{-65}{17}$$
8. **Final ordered pair:**
$$\left(\frac{8}{17}, \frac{-65}{17}\right)$$
**Answer:** The point on the line at $x = \frac{8}{17}$ is $\boxed{\left(\frac{8}{17}, \frac{-65}{17}\right)}$.