Question

Ordered pairs: 2, 10 3, 16 6, 30
The stretch of a spring in millimeters is proportional to the weight in grams attached to the end of the spring. Find the unit rate.
______ mm per gram

Answer 1

can u explain it simple

Answer 2

Ordered Pairs: 2, 14 3, 21 4, 28
Using the points shown in the graph, identify the constant of proportionality for this graph.
k = ____

Answer 3

To find the unit rate of stretch of the spring in millimeters per gram, we can calculate the rate using the provided ordered pairs (weight in grams, stretch in millimeters):

1. From the first ordered pair (2, 10):
\[
\text{Unit rate} = \frac{\text{stretch}}{\text{weight}} = \frac{10 \text{ mm}}{2 \text{ g}} = 5 \text{ mm/g}
\]

2. From the second ordered pair (3, 16):
\[
\text{Unit rate} = \frac{16 \text{ mm}}{3 \text{ g}} \approx 5.33 \text{ mm/g}
\]

3. From the third ordered pair (6, 30):
\[
\text{Unit rate} = \frac{30 \text{ mm}}{6 \text{ g}} = 5 \text{ mm/g}
\]

Now, we can summarize the unit rates obtained:

- From (2, 10) → 5 mm/g
- From (3, 16) → approximately 5.33 mm/g
- From (6, 30) → 5 mm/g

The unit rates are not consistent, indicating a linear relationship between weight and spring stretch. To find a more accurate overall unit rate, we can average the consistent values or choose the common unit rate seen in two out of the three ordered pairs.

In this case, we see that two of the ordered pairs give us a unit rate of 5 mm/g, which will be taken as the representative unit rate.

Thus, the unit rate for the stretch of the spring is:
\[
\boxed{5 \text{ mm per gram}}
\]

Answer 4

Sure! To find the unit rate of how much the spring stretches for every gram of weight, we look at the ordered pairs you provided. Each pair tells us how many millimeters the spring stretches (the second number) for a certain weight in grams (the first number).

Here’s how to calculate the unit rate for each pair:

1. **For the pair (2, 10)**:
- Weight: 2 grams
- Stretch: 10 mm
- Unit rate = Stretch / Weight = \( \frac{10 \text{ mm}}{2 \text{ g}} = 5 \text{ mm/g} \)

2. **For the pair (3, 16)**:
- Weight: 3 grams
- Stretch: 16 mm
- Unit rate = Stretch / Weight = \( \frac{16 \text{ mm}}{3 \text{ g}} \approx 5.33 \text{ mm/g} \)

3. **For the pair (6, 30)**:
- Weight: 6 grams
- Stretch: 30 mm
- Unit rate = Stretch / Weight = \( \frac{30 \text{ mm}}{6 \text{ g}} = 5 \text{ mm/g} \)

Now, most of the pairs give us a unit rate of 5 mm/g. The second pair gives a slightly higher rate (about 5.33 mm/g), but the other two pairs show that the unit rate is 5 mm for every gram.

So, we can conclude that the average unit rate is approximately \( \boxed{5 \text{ mm per gram}} \). This means for every gram of weight, the spring stretches about 5 millimeters.

Answer 5

To find the constant of proportionality \( k \) based on the ordered pairs you provided, we can calculate \( k \) using the formula:

\[
k = \frac{\text{Output}}{\text{Input}}
\]

with each ordered pair representing (input, output) as (weight, stretch).

Let's analyze each ordered pair:

1. **For the pair (2, 14)**:
\[
k = \frac{14}{2} = 7
\]

2. **For the pair (3, 21)**:
\[
k = \frac{21}{3} = 7
\]

3. **For the pair (4, 28)**:
\[
k = \frac{28}{4} = 7
\]

In all cases, the constant of proportionality \( k \) is the same. Thus, we can conclude that:

\[
k = 7
\]

So, the constant of proportionality for this graph is \( \boxed{7} \). This means that for every unit of input, the output (or stretch of the spring) increases by 7 units.