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To solve this problem, we need to use the point-slope form of the equation of a line, which is:

\[
y - y_1 = m(x - x_1)
\]

Where:
- \( m \) is the slope of the line (which is given as \( \frac{2}{5} \)),
- \( (x_1, y_1) \) is a point on the line (which is given as \( (5, -5) \)).

Substituting the given values into the point-slope form:

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

Simplifying this:

\[
y + 5 = \frac{2}{5}(x - 5)
\]

Now, distribute the slope \( \frac{2}{5} \) on the right side:

\[
y + 5 = \frac{2}{5}x - \frac{10}{5}
\]

\[
y + 5 = \frac{2}{5}x - 2
\]

Finally, subtract 5 from both sides to solve for \( y \):

\[
y = \frac{2}{5}x - 2 - 5
\]

\[
y = \frac{2}{5}x - 7
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = \frac{2}{5}x - 7
\]

### Do you have any questions, or would you like further details?

Here are five related questions to expand on this topic:
1. How would you find the equation of a line if given two points instead of the slope and a point?
2. What is the significance of the slope in a linear equation?
3. How do you interpret the y-intercept in the context of a graph?
4. How would the equation change if the slope were negative?
5. How can you graph this equation on a coordinate plane?

**Tip:** Always remember that in the slope-intercept form \( y = mx + b \), the \( m \) represents the slope, and the \( b \) is the y-intercept, the point where the line crosses the y-axis.

Mary has to write a linear function that has a slope of 2/5 and passes through the point (5, -5). What is the equation of the line in slope-intercept form?

Learn how to write the equation of a line in slope-intercept form when given a slope of 2/5 and a point through which it passes, (5, -5). This guide covers the use of point-slope and slope-intercept forms to derive the equation.

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