For this case we have:
By definition, two points are needed to find the equation of a line. We have a series of points given by:
[tex](x, y) = (time, cost)[/tex]
We chose two points:
[tex](t1, c1) = (1,180)\\(t2, c2) = (2,240)[/tex]
By definition, the formula of the slope is given by:
[tex]m =\frac{(c2-c1)}{(t2-t1)}[/tex]
Substituting:
[tex]m =\frac{240-180}{2-1}[/tex]
[tex]m =\frac{60}{1}\\m = 60[/tex]
Being a line of the form [tex]y = ax + b[/tex], we substitute a point and the slope found to find the cut point b.
[tex]180 = 60 * 1 + b\\180 = 60 + b\\b = 180-60\\b = 120[/tex]
Thus, the equation of the line is given by:
[tex]y = 60x + 120[/tex]
Answer:
Option C
