To find the equation of the line that passes through the points $(3, 0)$ and $(8, -2)$, we follow these steps:

1. Find the slope ($m$):

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

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

Substituting the given points $(3, 0)$ and $(8, -2)$:

$m = \frac{-2 - 0}{8 - 3} = \frac{-2}{5}$

Thus, the slope is:

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

2. Use the point-slope form:

The point-slope form of a line is:

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

We can use either of the given points. Using $(3, 0)$:

$y - 0 = -\frac{2}{5}(x - 3)$

This simplifies to:

$y = -\frac{2}{5}(x - 3)$

3. Fully simplified point-slope form:

The final equation is:

$y = -\frac{2}{5}(x - 3)$

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

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Related Questions:

1. How would the equation change if written in slope-intercept form?
2. What is the significance of the slope in the context of this line?
3. Could this line be written in standard form? If so, how?
4. How do you graph a line using the point-slope form?
5. What happens to the slope if the points are reversed?

Tip:

When using the point-slope form, always double-check the slope calculation to ensure precision.