Answer :
Given:
The two points are (-2,3) and (-4,-2).
To find:
The gradient of the line segment between the given points.
Solution:
The gradient is also known as slope.
The slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The endpoints of the line segment are (-2,3) and (-4,-2). So, the gradient of the line is
[tex]m=\dfrac{-2-3}{-4-(-2)}[/tex]
[tex]m=\dfrac{-5}{-4+2}[/tex]
[tex]m=\dfrac{-5}{-2}[/tex]
[tex]m=\dfrac{5}{2}[/tex]
Therefore, the gradient of the given line segment is [tex]m=\dfrac{5}{2}[/tex].