A local bakery buys their flour in bulk. The relationship between the cost of the flour and its weight is shown in the graph below.
Is the relationship shown a direct variation? Explain your reasoning using complete sentences.
The point (1, 0.75) is on this graph. What does this ordered pair represent?
Approximately how much does the bakery pay for 40 pounds of flour?
I'm sure it is direct variation, as long as y(0) = 0
If not, then it's not direct variation, and you have to add a constant.
So work your magic
To determine if the relationship shown in the graph is a direct variation, we need to examine the shape and behavior of the graph.
A direct variation is a relationship between two variables where their values are directly proportional to each other. In other words, as one variable increases, the other also increases by the same factor. This can be represented by a straight line through the origin (0,0) in a graph.
Looking at the graph provided, we can see that it is a straight line passing through the origin (0,0). This indicates that as the weight of the flour increases, the cost also increases proportionally. Therefore, the relationship shown in the graph is indeed a direct variation.
Now, let's analyze the given ordered pair (1, 0.75). In this case, the first number, 1, represents the weight of the flour in pounds, while the second number, 0.75, represents the cost of the flour in some currency unit (e.g., dollars).
Hence, the ordered pair (1, 0.75) represents that when the bakery purchases 1 pound of flour, the cost is 0.75 currency units. This information allows us to understand the cost of the flour depending on its weight.
To determine how much the bakery pays for 40 pounds of flour, we can use the information from the graph.
First, we need to find the corresponding cost for 40 pounds by using the graph. We can see that for every 1 pound increase in weight, the cost increases by 0.75 units. So, to find the cost of 40 pounds, we multiply the weight (40 pounds) by the cost ratio (0.75 units/1 pound):
40 pounds * (0.75 units/1 pound) = 30 units.
Therefore, the bakery would pay approximately 30 units for 40 pounds of flour.