To write the equation of a line in point-slope form, we first need to find the slope $m$ using the two given points: $(1, 5)$ and $(-1, -5)$.

Step 1: Find the slope $m$

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

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

Using the points $(1, 5)$ and $(-1, -5)$:

$m = \frac{-5 - 5}{-1 - 1} = \frac{-10}{-2} = 5$

So, the slope of the line is $m = 5$.

Step 2: Use the point-slope form equation

The point-slope form of a line is:

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

We can use either point. Let's use $(1, 5)$:

$y - 5 = 5(x - 1)$

This is the equation in point-slope form.

Step 3: Alternative point-slope equation using the second point

If we use the other point $(-1, -5)$, the equation would look like:

$y + 5 = 5(x + 1)$

Both forms represent the same line, just written using different points.

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Do you want to convert this to slope-intercept form, provide more details, or have any questions?

Here are 5 related questions:

1. How do you convert point-slope form to slope-intercept form?
2. How do you find the equation if you are only given the slope and one point?
3. What are the different forms of linear equations, and when is each used?
4. How do you graph a line from the point-slope form equation?
5. Can point-slope form be used for vertical or horizontal lines?

Tip: The point-slope form is particularly useful when you know a point on the line and the slope, and you don't need to rearrange it right away into slope-intercept form.