Question

kennys class is having a holiday party, and he is in charge of bringing juice. he decides to bring powdered juice mix and add water to it at school. there is a proportional relationship between the volume of water kenny uses to make the juice (in liters), x, and the number of scoops of juice mix he uses, y. x (liters) | y (scoops) 5 | 10 6 | 12 7 | 14 8 | 16 what is the constant of proportionality? write your answer as a whole number or decimal. scoops per liter submit work it out

Explanation:

Step1: Recall the formula for proportionality

For a proportional relationship \( y = kx \), the constant of proportionality \( k \) is given by \( k=\frac{y}{x} \).

Step2: Calculate \( k \) using a data point

Take the first data point \( x = 5 \) liters and \( y = 10 \) scoops. Substitute into the formula: \( k=\frac{10}{5}=2 \). We can verify with other points, e.g., \( x = 6 \), \( y = 12 \), \( k=\frac{12}{6}=2 \), \( x = 7 \), \( y = 14 \), \( k=\frac{14}{7}=2 \), \( x = 8 \), \( y = 16 \), \( k=\frac{16}{8}=2 \). All give \( k = 2 \).

Answer:

2