Step 1: Understanding the problem
The problem gives an initial point (0, 3000) which means when the price is $0, 3000 gallons of milk are sold. There's also information about the rate of decrease in the amount of milk sold for every unit increase in price. The amount of milk sold decreases by 500 gallons for every $1 increase in price.
Step 2: Determining the linear function
This situation can be modeled using a linear function of the form y = mx + b, where y is the amount of milk sold, x is the price, m is the slope of the line (or the change in y divided by the change in x), and b is the y-intercept (or the value of y when x = 0).
In this case, the slope (m) is -500 (since the amount of milk sold decreases by 500 gallons for every $1 increase in price) and the y-intercept (b) is 3000.
Hence the linear function is y = -500x + 3000.
Step 3: Plotting the function on a graph
You would start by plotting the initial point (0, 3000) on the graph. This represents the situation where the price is $0 and hence 3000 gallons of milk are sold.
Next, using the slope, we know that the amount of milk sold decreases by 500 gallons for every $1 increase in price. This means that for every step we move to the right on the x-axis (representing an increase in price), we move 500 units down on the y-axis (representing a decrease in the amount of milk sold).
By plotting these points and drawing the line that passes through them, you would obtain a graphical representation of the relationship between price and the amount of milk sold as described by the linear function.
Step 4: Interpretation of the graph
The graph would show a downwards sloping line starting at the point (0,3000): as the price increases (move to the right along the x-axis), the amount of milk sold decreases (moves down along the y-axis). This is consistent with the negative correlation between price and quantity sold that is described in the problem.
It's important to note that this model assumes that the relationship between price and quantity sold is linear, which might not be the case in the real world where other factors could impact consumer's buying behavior.