To find the equation of the line that passes through the point $(5, 0)$ and has a slope of $\frac{2}{5}$, we can use the point-slope form of the equation of a line, which is:

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

where:

• $(x_1, y_1)$ is the point the line passes through, and
• $m$ is the slope of the line.

Substituting $x_1 = 5$, $y_1 = 0$, and $m = \frac{2}{5}$ into the equation:

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

Simplifying this:

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

Expanding the right-hand side:

$y = \frac{2}{5}x - \frac{10}{5}$

$y = \frac{2}{5}x - 2$

Thus, the equation of the line is:

$y = \frac{2}{5}x - 2$

Let me know if you need further details or have any questions!

Here are 5 related questions for further exploration:

1. What is the slope-intercept form of the equation of a line?
2. How do you convert the point-slope form into standard form?
3. What is the meaning of slope in a real-world context?
4. How can you find the slope of a line from two points?
5. What happens to the equation of the line if the slope is negative?

Tip: Always ensure the slope is in the simplest form before using it in the equation to avoid unnecessary complications!