Variables h and c can be related by the equation of a line.
Let's define c (cost) as the dependent variable and h (hours) as the independent variable.
The slope of a line (m) that passes through the points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
In this case, the line passes through the points (1, 187) and (2, 259), then its slope is:
[tex]m=\frac{259-187}{2-1}=72[/tex]
In the context of this problem, the rate per hour coincides with the slope of the line, then:
rate per hour = 72 $/hour
The equation will have the form:
c = m*h + b
where b is the initial cost
Substituting with m = 72 and the point (1, 187) we get:
187 = 72*1 + b
187 - 72 = b
115 = b
initial cost = $115
