To identify the graph that shows the relationship between the weight of salami Jayson bought and the cost, we can establish a clear linear relationship.
First, we need to convert the weight of salami into a single number. Jayson bought \(1 \frac{1}{2}\) pounds of salami, which can be converted to a decimal: \[ 1 \frac{1}{2} = 1 + 0.5 = 1.5 \text{ pounds} \]
Next, we know that Jayson spent $3.75 for 1.5 pounds of salami. To find the price per pound, we can use the formula: \[ \text{Price per pound} = \frac{\text{Total Cost}}{\text{Weight in pounds}} = \frac{3.75}{1.5} = 2.50 \text{ per pound} \]
Now, if we plot this on a graph, we can identify the axes:
- \(x\)-axis could represent the weight of salami in pounds, and
- \(y\)-axis could represent the total cost in dollars.
We can create key points for the graph:
- At \(0\) pounds, the cost is \(0\) dollars (origin point).
- At \(1.5\) pounds, the cost is \(3.75\) dollars.
From this, we can infer that the relationship will be linear, with the line starting at the origin (0, 0) and rising to the point (1.5, 3.75).
If you want to identify a specific graph from a set of options, look for a straight line that passes through:
- The origin (0, 0)
- The point (1.5, 3.75)
This line should have a positive slope, indicating that as weight increases, cost increases proportionally. The slope can be calculated as \[ \text{slope} = \frac{3.75 - 0}{1.5 - 0} = 2.5 \] Thus, any graph relevant to Jayson’s purchase should clearly reflect this increasing linear relationship according to the data provided.
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