Question

name date class lesson 7 1. there is a proportional relationship between the volume of a sample of helium in liters and the mass of that sample in grams. if the mass of a sample is 5 grams, its volume is 28 liters. (5, 28) is shown on the graph below. graph with volume (liters) on y - axis and mass (grams) on x - axis, with point (5,28) plotted

Explanation:

Assuming the question is to find the constant of proportionality (unit rate) or to write the equation of the proportional relationship. Let's solve for the constant of proportionality first.

Step1: Recall the formula for proportional relationship

For a proportional relationship \( y = kx \), where \( y \) is volume (liters), \( x \) is mass (grams), and \( k \) is the constant of proportionality. We know a point \((x, y)=(5, 28)\).

Step2: Calculate the constant of proportionality \( k \)

Using the formula \( k=\frac{y}{x} \), substitute \( x = 5 \) and \( y = 28 \). So \( k=\frac{28}{5}=5.6 \). This means the equation is \( y = 5.6x \), where for each gram of mass, the volume is 5.6 liters.

If the question was to find the volume for a certain mass or mass for a certain volume, we can use this constant. For example, if we want to find the volume when mass is \( x \) grams, we use \( y = 5.6x \).

Answer:

The constant of proportionality is \( \boldsymbol{5.6} \) liters per gram, and the equation of the proportional relationship is \( \boldsymbol{y = 5.6x} \) (where \( y \) is volume in liters and \( x \) is mass in grams).