To determine the slope of the line represented by the equation [tex]\( y = \frac{4}{5} x - 3 \)[/tex], we need to identify the coefficient of [tex]\( x \)[/tex].
This equation is given in the slope-intercept form [tex]\( y = mx + b \)[/tex], where:
- [tex]\( m \)[/tex] is the slope of the line,
- [tex]\( b \)[/tex] is the y-intercept (the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]).
In the given equation [tex]\( y = \frac{4}{5} x - 3 \)[/tex], the coefficient [tex]\( \frac{4}{5} \)[/tex] is the slope. Therefore, [tex]\( m = \frac{4}{5} \)[/tex].
Thus, the slope of the line is [tex]\(\frac{4}{5}\)[/tex].
Among the given choices:
- [tex]\( -3 \)[/tex]
- [tex]\( -\frac{4}{5} \)[/tex]
- [tex]\( \frac{4}{5} \)[/tex]
- [tex]\( 3 \)[/tex]
The correct answer is:
[tex]\[
\frac{4}{5}
\][/tex]
