Answer:
The slope is undefined because the x value is same and what we have will be a vertical line through the point x = -4
Explanation:
Here, we want to get the slope between the points (-4,-1) and (-4,3)
Mathematically, we can do this by using the slope equation below:
![m=(y^(2)-y^(1) )/(x^(2)-x^(1) )](https://img.qammunity.org/2023/formulas/mathematics/high-school/dtzshgr35x8oq7wsdr28y1j60a0zuqf9ew.png)
The coordinates with the subscript 1 represents the first point, while the coordinates with the subscript 2 represents the second point
We have that as follows:
![x^(1) =-4](https://img.qammunity.org/2023/formulas/mathematics/high-school/9hb6tyocm50npm7zyhtr6i8176q0zmrt25.png)
![y^(1) =-1](https://img.qammunity.org/2023/formulas/mathematics/high-school/gtqcrlsjfxtklchkekpu6lahidmnwldm0e.png)
![x^(2) =-4](https://img.qammunity.org/2023/formulas/mathematics/high-school/bqlztfzbhd5a6pqd3yllwt9sbdu9rvepum.png)
![y^(2) =3](https://img.qammunity.org/2023/formulas/mathematics/high-school/dlp8vp4fasuna27xuv63c6zf4bxxn1f82j.png)
Now, we susbtitute the values into the slope equation above:
![m=(3+1)/(-4+4) =(4)/(0)](https://img.qammunity.org/2023/formulas/mathematics/high-school/6skwiaxjm3lpxn1duntwvvc3tqvz9gc6mn.png)
= Undefined.
The slope is undefined because the x value is same and what we have will be a vertical line through the point x = -4