To determine the slope of the line represented by the equation [tex]\( y = \frac{4}{5}x - 3 \)[/tex], let's break it down step-by-step:
1. First, recognize that the given equation is in the slope-intercept form, which is [tex]\[ y = mx + b \][/tex].
2. In the slope-intercept form, [tex]\( m \)[/tex] is the slope of the line, and [tex]\( b \)[/tex] is the y-intercept.
3. By comparing the given equation [tex]\( y = \frac{4}{5}x - 3 \)[/tex] with the slope-intercept form [tex]\( y = mx + b \)[/tex], we can identify the values of [tex]\( m \)[/tex] and [tex]\( b \)[/tex]:
- The coefficient of [tex]\( x \)[/tex] is [tex]\( \frac{4}{5} \)[/tex], which means [tex]\( m = \frac{4}{5} \)[/tex].
- The constant term is [tex]\( -3 \)[/tex], which means [tex]\( b = -3 \)[/tex] (though for this problem, we only need to focus on the slope).
4. Therefore, the slope of the line is [tex]\( \frac{4}{5} \)[/tex].
So, the correct answer is:
[tex]\[ \frac{4}{5} \][/tex]
