1 Answer

Michael Butscher · Answer 1 · 2020-12-29T14:00:54+0000

Hello!

The answer is:

The first option,

y=-(1)/(2)x-3;x<-2

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

y=-(1)/(2)x-3

With,

x<-2

- Finding the y-axis component when x is equal to -2, we have:

$y=-(1)/(2)*(-2)-3\\y=1-3=-2$

We have that one of the points of the segments is located at (-2,-2)

- Finding the "x" intercept, we have:

$0=-(1)/(2)x-3\\\\(1)/(2)x=-3\\\\x=2*-3=-6$

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:

Slope=-(1)/(2)

x-axis_(interception)=-6

Point(-2,-2)

and from the inequality, we know that the segment exists from -∞ to -2.

Have a nice day!