The initial value of the function is $110. The equation of the function is y = 35x + 110, where x represents the number of cubic yards of mulch and y represents the total cost.
To find the initial value, we need to determine the y-intercept of the linear relationship between the number of cubic yards of mulch and the total cost.
In this case, the y-intercept represents the total cost when the number of cubic yards of mulch is 0.
From the given data, we can see that when x = 0 (number of cubic yards of mulch), the total cost is $110. This means that the initial value (y-intercept) is $110.
To write the equation of the function, we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. Since the relationship is linear, we can calculate the slope by finding the change in y divided by the change in x for any two points on the line.
Let's choose the first and second data points: (2, 110) and (3, 145).
Slope (m) = (145-110)/(3-2) = 35/1 = 35.
Using the slope and y-intercept, we can write the equation of the function as: y = 35x + 110.
This equation represents the relationship between the number of cubic yards of mulch (x) and the total cost (y).