To find the unit rate of stretch per weight for a spring, we first need to establish the relationship between the stretch of the spring (in millimeters) and the weight attached to it (in grams).
This relationship can be described with the formula:
\[ \text{Stretch} = k \times \text{Weight} \]
where \(k\) is the constant of proportionality and represents the stretch per gram of weight.
The unit rate in this case would be the value of \(k\), which shows how many millimeters the spring stretches for each gram of weight added.
To determine \(k\), you would need to have specific data points for the weight and corresponding stretch distances. For instance, if you have a spring that stretches 10 mm when a weight of 50 grams is attached:
\[ k = \frac{\text{Stretch}}{\text{Weight}} = \frac{10 \text{ mm}}{50 \text{ g}} = 0.2 \text{ mm/g} \]
This means the unit rate (or the stretch per gram) is 0.2 mm per gram.
To find the unit rate in a specific scenario, simply take the stretch in millimeters and divide it by the weight in grams:
\[ k = \frac{\text{Stretch (mm)}}{\text{Weight (g)}} \]
If you provide specific values for stretch and weight, I can help you calculate the unit rate based on that information!