To find the slope of the line represented by the equation [tex]\( y = -\frac{2}{3} - 5x \)[/tex], we need to identify the slope-intercept form of a linear equation, which is:
[tex]\[ y = mx + b \][/tex]
Here, [tex]\( m \)[/tex] represents the slope of the line, and [tex]\( b \)[/tex] is the y-intercept. In this form, the coefficient of [tex]\( x \)[/tex] is the slope.
The given equation is:
[tex]\[ y = -\frac{2}{3} - 5x \][/tex]
We can rewrite the equation to fit the slope-intercept form [tex]\( y = mx + b \)[/tex]:
[tex]\[ y = -5x - \frac{2}{3} \][/tex]
Now, we compare it to the standard form [tex]\( y = mx + b \)[/tex]:
[tex]\[ y = -5x - \frac{2}{3} \][/tex]
[tex]\[ y = mx + b \][/tex]
From this comparison, we can see that:
- The coefficient of [tex]\( x \)[/tex] is [tex]\(-5\)[/tex], which means the slope, [tex]\( m \)[/tex], is [tex]\(-5\)[/tex].
Therefore, the slope of the line is:
[tex]\[ \boxed{-5} \][/tex]
