Step 1: Find the slope of the line

The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
For the given points $(-1, -7)$ and $(1, 7)$:
$m = \frac{7 - (-7)}{1 - (-1)} = \frac{7 + 7}{1 + 1} = \frac{14}{2} = 7$
Thus, the slope $m = 7$.

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Step 2: Write the equation in point-slope form

The point-slope form of a line is:
$y - y_1 = m(x - x_1)$
Using the slope $m = 7$ and one of the points, say $(-1, -7)$:
$y - (-7) = 7(x - (-1))$
Simplify:
$y + 7 = 7(x + 1)$

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Step 3: Final equation in simplified point-slope form

$y + 7 = 7(x + 1)$

This is the equation of the line in point-slope form.

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Do you have any questions or need further clarification?

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Related Questions

1. How do you convert a point-slope equation to slope-intercept form?
2. What is the general form of a linear equation?
3. How do you find the slope of a vertical or horizontal line?
4. How do you check if a point lies on a given line?
5. What is the distance between the two given points?

Tip: Always simplify your slope first before plugging it into the point-slope equation to avoid algebra mistakes!