For this case we have:
By definition, to find the slope of a line you need two points where the line passes.
Looking at the graph we can see that the line passes through the following points:
[tex](x, y) = (0, -5)\\(x, y) = (2.5,0)\\(x, y) = (5,5)[/tex]
We chose two points:
[tex](x1, y1) = (2.5,0)\\(x2, y2) = (5,5)[/tex]
The equation of the slope is given by:
[tex]m =\frac{(y2-y1) }{(x2-x1)}[/tex]
Substituting we have:
[tex]m =\frac{(5-0)}{(5-2.5)}[/tex]
[tex]m =\frac{(5)}{(2.5)}[/tex]
[tex]m = 2[/tex]
On the other hand, the linear equation of a line is given by:
[tex]y = mx + b[/tex]
We substitute a point and the slope found to find the cut point b:
[tex]5 = 2 * 5 + b\\5 = 10 + b\\b = 5-10 \\b = -5[/tex]
Thus, the equation of the line is given by:
[tex]y = 2x-5[/tex]
Answer:
[tex]y = 2x-5[/tex]
Option D
