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!