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]
[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]
