What is the slope of the line represented by the equation [tex]y = \frac{4}{5}x - 3[/tex]?

A. [tex]-3[/tex]
B. [tex]-\frac{4}{5}[/tex]
C. [tex]\frac{4}{5}[/tex]
D. [tex]3[/tex]



Answer :

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]