To determine the slope of the line represented by the equation [tex]\( y = \frac{4}{5} x - 3 \)[/tex], we need to recall the general form of a linear equation in two variables, which is:
[tex]\[ y = mx + c \][/tex]
In this form:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( c \)[/tex] is the y-intercept of the line.
Given the equation [tex]\( y = \frac{4}{5} x - 3 \)[/tex], we can directly compare it with the standard form [tex]\( y = mx + c \)[/tex].
In the given equation:
- The term [tex]\( \frac{4}{5} \)[/tex] is the coefficient of [tex]\( x \)[/tex].
- The term [tex]\(-3\)[/tex] is the constant term, which represents the y-intercept but is not relevant to finding the slope.
Therefore, the slope [tex]\( m \)[/tex] of the line is the coefficient of [tex]\( x \)[/tex], which is [tex]\( \frac{4}{5} \)[/tex].
Hence, the correct answer is:
[tex]\[ \frac{4}{5} \][/tex]
