1. Determine the relationship:
   • The cook uses 2.5 cups of flour for each ounce of butter.
   • This relationship can be written as \(y = 2.5x\), where \(y\) is the amount of flour (cups) and \(x\) is the amount of butter (ounces).
2. Identify the correct graph:
   • The graph should show a linear relationship with a slope of 2.5.
   • For 1 ounce of butter, there should be 2.5 cups of flour.
   • For 2 ounces of butter, there should be 5 cups of flour, and so on.
3. Analyze the graphs:
   • Graph D shows a line that passes through the points (0,0), (2,5), (4,10), etc., which matches the relationship \(y = 2.5x\).

Supplemental Knowledge

A central tenant of algebra lies in understanding how two quantities relate, and graphically representing this relationship graphically. If one quantity changes at an equal pace with respect to another quantity, this relationship can be represented using linear functions.

Key Concepts:

Proportional Relationship:

A proportional relationship between two quantities means that they increase or decrease at the same rate.

This can be expressed as \(y = kx\), where \(k\) is the constant of proportionality.

Graphing Proportional Relationships:

The graph of a proportional relationship is a straight line that passes through the origin (0,0).

• The slope of the line represents the rate of change or the constant of proportionality.

Knowledge in Action

Think about how recipes work when it comes to cooking. Knowing that every ounce of butter requires 2.5 cups of flour helps with proportional thinking when adapting recipes based on available ingredients.

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