The equation of a linear function can be expressed in the slope-intercept form, which is given by:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
In this case, you mentioned a slope of \( \frac{4}{5} \) and a y-intercept of -6. Therefore, the equation that correctly represents this linear function is:
\[ y = \frac{4}{5}x - 6 \]
From the options you provided, the correct representation is:
y = four-fifths x minus 6.