To determine the slope of the line represented by the equation [tex]\( y = \frac{4}{5} x - 3 \)[/tex], we should recall the standard form of a linear equation, which is [tex]\( y = mx + b \)[/tex]. In this form, [tex]\( m \)[/tex] represents the slope of the line, and [tex]\( b \)[/tex] represents the y-intercept.
Here, the given equation is:
[tex]\[ y = \frac{4}{5} x - 3 \][/tex]
By comparing this with the standard form [tex]\( y = mx + b \)[/tex], we can clearly see that the coefficient of [tex]\( x \)[/tex] is [tex]\( \frac{4}{5} \)[/tex]. This coefficient is the slope [tex]\( m \)[/tex] of the line.
So, the slope of the line is:
[tex]\[ \frac{4}{5} \][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{4}{5}}
\][/tex]
