To find the slope of a line given by an equation in the slope-intercept form, we first need to understand the structure of this form. The slope-intercept form of a linear equation is:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( b \)[/tex] represents the y-intercept of the line.
Given the equation:
[tex]\[ y = \frac{2}{3} - 5x \][/tex]
we need to rewrite it in the slope-intercept form. Notice this equation is already in a form where the slope can be identified directly:
[tex]\[ y = -5x + \frac{2}{3} \][/tex]
Now, comparing it with the form [tex]\( y = mx + b \)[/tex]:
- The coefficient of [tex]\( x \)[/tex] is [tex]\( -5 \)[/tex].
- So, [tex]\( m = -5 \)[/tex].
Thus, the slope of the line represented by the equation [tex]\( y = \frac{2}{3} - 5x \)[/tex] is:
[tex]\[ -5 \][/tex]
Therefore, the correct answer is:
[tex]\[ -5 \][/tex]
