To write the equation of a line in slope-intercept form, which is given by the equation \( y = mx + b \), we need the slope (\( m \)) and the y-intercept (\( b \)).
Here, the slope \( m = -\frac{2}{5} \) and the line passes through the point \( (17, -6) \).
We can use the point-slope form of the equation of a line:
\[ y - y_1 = m(x - x_1) \]
Substituting \( m = -\frac{2}{5} \), \( x_1 = 17 \), and \( y_1 = -6 \):
\[ y - (-6) = -\frac{2}{5}(x - 17) \]
This simplifies to:
\[ y + 6 = -\frac{2}{5}(x - 17) \]
Now, distribute the slope on the right side:
\[ y + 6 = -\frac{2}{5}x + \frac{34}{5} \]
Next, we isolate \( y \) by subtracting 6 from both sides. Note that \( 6 \) can be written as \( \frac{30}{5} \):
\[ y = -\frac{2}{5}x + \frac{34}{5} - \frac{30}{5} \]
Combining the fractions gives:
\[ y = -\frac{2}{5}x + \frac{4}{5} \]
Thus, the equation of the line in slope-intercept form is:
\[ y = -\frac{2}{5}x + \frac{4}{5} \]