Hello!
The answer is:
The first option,
[tex]y=-\frac{1}{2}x-3;x<-2[/tex]
Why?
To answer the question, we need to look for an inequality that fits with the following description:
- Negative slope, since the segment "a" is decreasing.
- x- axis interception at x equal to -6
- One of its point is located at (-2,-2)
- The segment exists from -∞ to -2.
So, checking we have:
Firs option
[tex]y=-\frac{1}{2}x-3[/tex]
With,
[tex]x<-2[/tex]
- Finding the y-axis component when x is equal to -2, we have:
[tex]y=-\frac{1}{2}*(-2)-3\\y=1-3=-2[/tex]
We have that one of the points of the segments is located at (-2,-2)
- Finding the "x" intercept, we have:
[tex]0=-\frac{1}{2}x-3\\\\\frac{1}{2}x=-3\\\\x=2*-3=-6[/tex]
Also, (from the inequality and the graph) we know that, the given segment exists from the negative infinite numbers to -2.
Hence, we can know that the first option meets all the requirements:
[tex]Slope=-\frac{1}{2}[/tex]
[tex]x-axis_{interception}=-6[/tex]
[tex]Point(-2,-2)[/tex]
and from the inequality, we know that the segment exists from -∞ to -2.
Have a nice day!
