To find the rate of change, we can use the slope formula, which is:
rate of change = (y2 - y1) / (x2 - x1)
where x1, y1 represent the first point (2 hours and $9.50), and x2, y2 represent the second point (5 hours and $18.50).
rate of change = ($18.50 - $9.50) / (5 - 2) = $9 / 3 = $3 per hour
To find the initial value, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
where m is the rate of change (slope) and (x1, y1) is a point on the line.
y = $3x + b
We can use the first point (2 hours and $9.50) to find the value of b:
$9.50 = $3(2) + b
b = $9.50 - $6 = $3.50
So the equation of the line is:
y = $3x + $3.50
The rate of change means that for every additional hour of skating, the cost increases by $3. The initial value of $3.50 means that the cost of the skate rental fee is $3.50.