Sure! Let's solve the equation step-by-step to identify the slope and the y-intercept.
The given equation is:
[tex]\[ y = \frac{-x}{2} - 8 \][/tex]
This equation is in the slope-intercept form of a linear equation, which is generally written as:
[tex]\[ y = mx + b \][/tex]
Here:
- [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( b \)[/tex] represents the y-intercept of the line, which is the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is 0.
Comparing the given equation to the standard slope-intercept form:
[tex]\[ y = \frac{-x}{2} - 8 \][/tex]
We see that:
1. The coefficient of [tex]\( x \)[/tex] is [tex]\( \frac{-1}{2} \)[/tex], which means the slope [tex]\( m \)[/tex] is:
[tex]\[ m = -0.5 \][/tex]
2. The constant term is [tex]\( -8 \)[/tex], which means the y-intercept [tex]\( b \)[/tex] is:
[tex]\[ b = -8 \][/tex]
Thus, for the given equation [tex]\( y = \frac{-x}{2} - 8 \)[/tex]:
- The slope [tex]\( m \)[/tex] is [tex]\( -0.5 \)[/tex].
- The y-intercept [tex]\( b \)[/tex] is [tex]\( -8 \)[/tex].
So, the slope and y-intercept are:
[tex]\[ \text{slope} = -0.5 \][/tex]
[tex]\[ \text{y-intercept} = -8 \][/tex]
