Answer :
To determine the slope of the line given by the equation \( y = -\frac{2}{3} - 5x \), we need to identify the slope-intercept form of the equation of a line, which is given by the formula:
[tex]\[ y = mx + b \][/tex]
In this formula, \( m \) represents the slope of the line, and \( b \) represents the y-intercept (the point where the line crosses the y-axis).
Now, let's compare the given equation to the slope-intercept form:
[tex]\[ y = -\frac{2}{3} - 5x \][/tex]
We can rewrite the equation to make the comparison more straightforward:
[tex]\[ y = -5x - \frac{2}{3} \][/tex]
Here, we can see that the coefficient of \( x \) (which is the term directly in front of \( x \)) is \(-5\). This coefficient represents the slope \( m \) of the line.
Therefore, the slope of the line \( y = -\frac{2}{3} - 5x \) is \(-5\).
Hence, the correct answer is:
[tex]\(-5\)[/tex]
[tex]\[ y = mx + b \][/tex]
In this formula, \( m \) represents the slope of the line, and \( b \) represents the y-intercept (the point where the line crosses the y-axis).
Now, let's compare the given equation to the slope-intercept form:
[tex]\[ y = -\frac{2}{3} - 5x \][/tex]
We can rewrite the equation to make the comparison more straightforward:
[tex]\[ y = -5x - \frac{2}{3} \][/tex]
Here, we can see that the coefficient of \( x \) (which is the term directly in front of \( x \)) is \(-5\). This coefficient represents the slope \( m \) of the line.
Therefore, the slope of the line \( y = -\frac{2}{3} - 5x \) is \(-5\).
Hence, the correct answer is:
[tex]\(-5\)[/tex]
