Question

1 the graph shows the proportional relationship between grams of protein and cups of milk. a. what is the constant of proportionality for the relationship between grams of protein and cups of milk? b. what does the point (0, 0) mean in this situation? c. what does the point (4, 32) mean in this situation? protein (grams) milk (cups)

Explanation:

Part a:

Step1: Recall constant of proportionality formula

For a proportional relationship \( y = kx \), the constant of proportionality \( k=\frac{y}{x} \), where \( y \) is grams of protein and \( x \) is cups of milk.

Step2: Use a point from the graph (e.g., (4,32))

Substitute \( x = 4 \) and \( y = 32 \) into \( k=\frac{y}{x} \). So \( k=\frac{32}{4}=8 \).

In the context of this proportional relationship (grams of protein vs. cups of milk), the point \((0,0)\) means when there are \( 0 \) cups of milk, there are \( 0 \) grams of protein. This makes sense because without any milk, there is no protein from the milk source.

In the proportional relationship between grams of protein (y - axis) and cups of milk (x - axis), the point \((4,32)\) means that when there are \( 4 \) cups of milk, there are \( 32 \) grams of protein. This is interpreted by taking the x - value (4 cups of milk) and the corresponding y - value (32 grams of protein) from the point.

Answer:

The constant of proportionality is \( 8 \).

Part b: