The slope-intercept form of a linear equation is given by the formula:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
Given:
- Slope \( m = -\frac{4}{5} \)
- Y-intercept \( b = \frac{6}{5} \)
Substituting the values into the slope-intercept formula gives:
\[ y = -\frac{4}{5}x + \frac{6}{5} \]
This is the equation in slope-intercept form.
If you want to express the equation with a common denominator, you can also write it as:
\[ y = -\frac{4}{5}x + \frac{6}{5} \]
In this form, it already uses proper fractions. If you desire integers or improper fractions, you can rewrite it but this fraction representation is already in simplest form.
Therefore, the final equation is:
\[ y = -\frac{4}{5}x + \frac{6}{5} \]