To determine which equation represents a linear function with a given slope and y-intercept, let's recall the general form of a linear equation:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] represents the slope,
- [tex]\( b \)[/tex] represents the y-intercept.
Given:
- The slope [tex]\( m \)[/tex] is [tex]\(\frac{4}{5} \)[/tex],
- The y-intercept [tex]\( b \)[/tex] is [tex]\(-6 \)[/tex].
Using these values, we substitute [tex]\( m \)[/tex] and [tex]\( b \)[/tex] into the general form:
[tex]\[ y = \frac{4}{5} x + (-6) \][/tex]
This simplifies to:
[tex]\[ y = \frac{4}{5} x - 6 \][/tex]
Now, we can look at the given choices to find the one that matches this equation:
1. [tex]\( y = -6x + \frac{4}{5} \)[/tex]
2. [tex]\(y = \frac{4}{5} x - 6 \)[/tex]
3. [tex]\(y = \frac{4}{5} x + 6 \)[/tex]
4. [tex]\( y = 6 x + \frac{4}{5} \)[/tex]
The correct equation is:
[tex]\[ y = \frac{4}{5} x - 6 \][/tex]
Thus, the equation that represents a linear function with a slope of [tex]\(\frac{4}{5}\)[/tex] and a y-intercept of -6 is:
[tex]\[ y = \frac{4}{5} x - 6 \][/tex]
which corresponds to the second choice. Therefore, the answer is:
[tex]\[ \boxed{2} \][/tex]
