To determine the slope of the line represented by the equation [tex]\( y = \frac{2}{3} - 5x \)[/tex], let's analyze the equation in its standard slope-intercept form.
The standard form of a linear equation is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
Given the equation:
[tex]\[ y = \frac{2}{3} - 5x \][/tex]
We can rewrite this equation in a form that more clearly resembles the slope-intercept form. Note that the order of terms doesn't affect the slope or intercept:
[tex]\[ y = -5x + \frac{2}{3} \][/tex]
Here, the equation is in the form [tex]\( y = mx + b \)[/tex]:
- [tex]\( m \)[/tex] is the coefficient of [tex]\( x \)[/tex], which is [tex]\(-5\)[/tex].
- [tex]\( b \)[/tex] is the constant term, which is [tex]\(\frac{2}{3}\)[/tex].
Therefore, the slope [tex]\( m \)[/tex] of the line is [tex]\(-5\)[/tex].
Among the given choices:
- [tex]\( -5 \)[/tex]
- [tex]\( \frac{2}{3} \)[/tex]
- [tex]\( \frac{2}{3} \)[/tex]
- [tex]\( 5 \)[/tex]
The correct answer is:
[tex]\[ -5 \][/tex]
