To find the equation of the line that passes through $(7, 8)$ and $(9, -9)$, we follow these steps:

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Step 1: Calculate the slope ($m$):

The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

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

Substituting the points $(7, 8)$ and $(9, -9)$:

$m = \frac{-9 - 8}{9 - 7} = \frac{-17}{2}$

So, the slope is:

$m = -\frac{17}{2}$

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Step 2: Use the point-slope form of the line equation:

The point-slope form of a line is:

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

Using the point $(7, 8)$ and the slope $m = -\frac{17}{2}$:

$y - 8 = -\frac{17}{2}(x - 7)$

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Final Answer:

The equation of the line in point-slope form is:

$y - 8 = -\frac{17}{2}(x - 7)$

This is the fully simplified point-slope form of the equation.

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Would you like details on converting this equation to slope-intercept or standard form?

Related Questions:

1. How can this line equation be converted to slope-intercept form?
2. What are some properties of lines with negative slopes like this one?
3. How do we handle vertical or horizontal lines in point-slope form?
4. Can this line equation be graphed without further simplification?
5. What is the midpoint of the segment connecting the given points?

Tip:

When working with slopes involving fractions, ensure all calculations stay consistent to avoid errors with signs or division.