Slope: -500
y-intercept: 3000
x-intercept: 6 Interpretation of the Intercepts: See solution. Graph:
Practice makes perfect
We are told that the amount of milk sold on the farm decreases by 500 gallons for each increase of $1 in price. We can use this information to write the rate of change.
-500 gallons/1 dollar ⇒ m=-500Now we have the slope of the function. To graph the function, we also need the y-intercept. We are given that m( 0)= 3000, so we can identify the y-intercept as ( 0, 3000). Now we have enough information to graph the function.
Notice that our domain is being restricted to the first quadrant because we cannot sell a negative number of gallons of milk and we cannot sell things for a negative amount of money.
Interpretation of the y-intercept
We already know that the y- is (0,3000). We know that x represents the cost of each gallon of milk and m(x) represents the number of gallons of milk sold. Therefore, the point (0,3000) tells us that if the milk is free, 3000 gallons would be taken.
Interpretation of the x-intercept
We can see from the graph that the x-intercept is (6,0). This means that if the price of the gallon is $6, then no gallons are sold.
