The slope of a line is the average rate of change of the line.
The graph that represents [tex]\mathbf{y = x - 2}[/tex] is graph (a)
The line equation is given as:
[tex]\mathbf{y = x - 2}[/tex]
To do this, we simply test the options until we get the correct graph
(a) Line that passes through (-2,-4) and (0,-2)
This means that:
[tex]\mathbf{(x_1,y_1) = (-2,-4)}[/tex]
[tex]\mathbf{(x_2,y_2) = (0,-2)}[/tex]
Substitute values for x1 and y1 in [tex]\mathbf{y = x - 2}[/tex]
[tex]\mathbf{-4 = -2 - 2}[/tex]
[tex]\mathbf{-4 = -4}[/tex]
This point is true for [tex]\mathbf{y = x - 2}[/tex]
Substitute values for x2 and y2 in [tex]\mathbf{y = x - 2}[/tex]
[tex]\mathbf{-2 = 0 - 2}[/tex]
[tex]\mathbf{-2 = - 2}[/tex]
This point is also true for [tex]\mathbf{y = x - 2}[/tex]
Hence, the graph that represents [tex]\mathbf{y = x - 2}[/tex] is graph (a)
See attachment for the graph of [tex]\mathbf{y = x - 2}[/tex]
Read more about linear functions at:
https://brainly.com/question/20286983
