To find the equation of the line passing through the points $(-1, -7)$ and $(1, 7)$ in point-slope form, we need to:

1. Calculate the slope (m) between the points using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ where $(x_1, y_1) = (-1, -7)$ and $(x_2, y_2) = (1, 7)$.

2. Substitute into point-slope form, $y - y_1 = m(x - x_1)$, using one of the points.

Step 1: Calculate the Slope

$m = \frac{7 - (-7)}{1 - (-1)} = \frac{7 + 7}{1 + 1} = \frac{14}{2} = 7$

Step 2: Write in Point-Slope Form

Using the point $(-1, -7)$: $y - (-7) = 7(x - (-1))$ This simplifies to: $y + 7 = 7(x + 1)$

So, the equation in point-slope form is: $y + 7 = 7(x + 1)$

You can enter this answer as the solution.

Would you like more details on this process or have any questions?

Here are five related questions to deepen understanding:

1. How do you convert the equation from point-slope form to slope-intercept form?
2. What is the y-intercept of this line?
3. How would the equation change if you used the other point $(1, 7)$ for the point-slope form?
4. Can you write the equation in standard form $Ax + By = C$?
5. What would the slope be if the points were $(-1, 7)$ and $(1, -7)$?

Tip: Point-slope form is very useful for quickly writing the equation of a line when you know the slope and one point on the line.