What is the slope of the line represented by the equation [tex]\( y = -\frac{2}{3} - 5x \)[/tex]?

A. [tex]\(-5\)[/tex]
B. [tex]\(-\frac{2}{3}\)[/tex]
C. [tex]\(\frac{2}{3}\)[/tex]
D. 5



Answer :

To determine the slope of the line represented by the equation [tex]\( y = -\frac{2}{3} - 5x \)[/tex], we need to understand the structure of a linear equation in the slope-intercept form, which is given by:

[tex]\[ y = mx + b \][/tex]

In this form:
- [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( b \)[/tex] represents the y-intercept, which is the point where the line intersects the y-axis.

In the given equation [tex]\( y = -\frac{2}{3} - 5x \)[/tex], let's reorganize it to match the slope-intercept form:

[tex]\[ y = -5x - \frac{2}{3} \][/tex]

Now it is clear that the equation is written as [tex]\( y = mx + b \)[/tex] with:
- [tex]\( m = -5 \)[/tex] (the coefficient of [tex]\( x \)[/tex])
- [tex]\( b = -\frac{2}{3} \)[/tex] (the constant term, which is the y-intercept)

Therefore, the slope [tex]\( m \)[/tex] of the line is [tex]\( -5 \)[/tex].

So, the correct answer is:

[tex]\[ \boxed{-5} \][/tex]