To find the equation of the line in point-slope form, we first need to follow these steps:

1. Find the slope (m):

The formula to calculate the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the coordinates $(-10, 1)$ and $(10, -9)$ into the formula:

$m = \frac{-9 - 1}{10 - (-10)} = \frac{-10}{20} = -\frac{1}{2}$

2. Point-slope form of the equation:

The point-slope form of the equation is:

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

Using the slope $m = -\frac{1}{2}$ and the point $(-10, 1)$, substitute into the formula:

$y - 1 = -\frac{1}{2}(x - (-10))$

Simplifying:

$y - 1 = -\frac{1}{2}(x + 10)$

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

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

Here are five related questions to explore further:

1. How do you convert from point-slope form to slope-intercept form?
2. What is the general formula for the equation of a line?
3. How can we graph the equation of a line given two points?
4. How do you determine the x- and y-intercepts from a linear equation?
5. What is the significance of the slope in real-world problems?

Tip: When finding the slope of a line between two points, ensure you're carefully subtracting the y-values and x-values in the correct order (y2 - y1, x2 - x1) to avoid sign mistakes!