To find the equation of line $s$, we need to follow these steps:

1. Determine the slope of line $s$: Since line $s$ is parallel to line $r$, they share the same slope. We first need to find the slope of line $r$.

   The equation of line $r$ is given as: $y - 9 = 3(x - 10)$ This is in point-slope form, where the slope $m = 3$.

   Therefore, the slope of line $s$ is also $3$.

2. Use the point-slope form to write the equation of line $s$: Line $s$ passes through the point $(-2, -7)$ and has a slope of 3. We use the point-slope form of a line equation: $y - y_1 = m(x - x_1)$ Substituting the point $(-2, -7)$ for $(x_1, y_1)$ and the slope $m = 3$, we get: $y - (-7) = 3(x - (-2))$ Simplifying this equation: $y + 7 = 3(x + 2)$ Distribute the 3 on the right-hand side: $y + 7 = 3x + 6$ Subtract 7 from both sides: $y = 3x + 6 - 7$ Simplifying further: $y = 3x - 1$

Thus, the equation of line $s$ in slope-intercept form is: $y = 3x - 1$

Would you like further details or have any questions?

Here are 5 related questions you might find useful:

1. How do you find the equation of a line perpendicular to a given line?
2. What is the difference between point-slope form and slope-intercept form?
3. How do you convert from standard form to slope-intercept form?
4. Can two lines be parallel if they have different slopes?
5. How do you find the slope of a line from its graph?

Tip: When two lines are parallel, their slopes are always equal.