To find the unit rate of the stretch of a spring in relation to the weight attached to it, we need to establish a relationship between the two variables: stretch (in millimeters) and weight (in grams).
If we say that the stretch of the spring \( S \) (in mm) is proportional to the weight \( W \) (in g), we can express this relationship mathematically as:
\[ S = kW \]
where \( k \) is the constant of proportionality, also known as the unit rate in this context.
To find the unit rate \( k \), you would need data on how much the spring stretches for a given weight. For example, if a weight of 100 grams causes the spring to stretch 50 mm, we can determine the unit rate:
\[ k = \frac{S}{W} = \frac{50 \text{ mm}}{100 \text{ g}} = 0.5 \text{ mm/g} \]
This means for every gram added to the spring, it stretches by 0.5 mm.
If you have specific values or a data set, you can substitute those values in to find the unit rate.