We are given two lines, $p$ and $q$, where line $q$ is parallel to line $p$. We know the following about line $p$:

$y = \frac{1}{7}x - 10$

Since line $q$ is parallel to line $p$, the slope of line $q$ is the same as the slope of line $p$. The slope of line $p$ is $\frac{1}{7}$.

Now, line $q$ passes through the point $(2, -1)$. To find the equation of line $q$, we will use the point-slope form of a line, which is:

$y - y_1 = m(x - x_1)$

where $m$ is the slope and $(x_1, y_1)$ is a point on the line. In this case, $m = \frac{1}{7}$, $x_1 = 2$, and $y_1 = -1$.

Substituting these values into the point-slope form:

$y - (-1) = \frac{1}{7}(x - 2)$

Simplify the equation:

$y + 1 = \frac{1}{7}(x - 2)$

Distribute the $\frac{1}{7}$:

$y + 1 = \frac{1}{7}x - \frac{2}{7}$

Now, subtract 1 from both sides to get the equation in slope-intercept form $y = mx + b$:

$y = \frac{1}{7}x - \frac{2}{7} - 1$

Convert $1$ to a fraction with a denominator of 7:

$y = \frac{1}{7}x - \frac{2}{7} - \frac{7}{7}$

Simplify:

$y = \frac{1}{7}x - \frac{9}{7}$

Thus, the equation of line $q$ is:

$y = \frac{1}{7}x - \frac{9}{7}$

Let me know if you would like further details or have any questions!

Here are 5 related questions:

1. How do you find the slope of a line from its equation?
2. What is the point-slope form of a line, and when is it useful?
3. How do you determine if two lines are parallel?
4. How can you convert a line's equation from point-slope form to slope-intercept form?
5. How would the equation change if line $q$ passed through a different point?

Tip: Parallel lines always have the same slope but different y-intercepts unless they are identical lines.