To determine the slope and the [tex]\( y \)[/tex]-intercept of the given equation [tex]\( y = -\frac{1}{3}x - 6 \)[/tex], let's break it down step-by-step.
1. The equation [tex]\( y = -\frac{1}{3}x - 6 \)[/tex] is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where:
- [tex]\( m \)[/tex] represents the slope.
- [tex]\( b \)[/tex] represents the [tex]\( y \)[/tex]-intercept.
2. Identify the slope ([tex]\( m \)[/tex]) from the equation:
- The term with [tex]\( x \)[/tex] is [tex]\( -\frac{1}{3}x \)[/tex].
- Therefore, the slope [tex]\( m \)[/tex] is [tex]\( -\frac{1}{3} \)[/tex].
3. Identify the [tex]\( y \)[/tex]-intercept ([tex]\( b \)[/tex]) from the equation:
- The constant term is [tex]\( -6 \)[/tex].
- Thus, the [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex] is [tex]\( -6 \)[/tex].
So, the slope is [tex]\( -\frac{1}{3} \)[/tex] and the [tex]\( y \)[/tex]-intercept is [tex]\( -6 \)[/tex].
Therefore, the correct answer is:
[tex]\[ -\frac{1}{3} ; -6 \][/tex]
This corresponds to the fourth answer choice:
[tex]\[ -1 / 3 ; -6 \][/tex]
So, the slope and [tex]\( y \)[/tex]-intercept are [tex]\( -\frac{1}{3} \)[/tex] and [tex]\( -6 \)[/tex] respectively, and the correct answer choice is:
[tex]\[ \text{Answer choice: 4} \][/tex]
