Question

a phone keeps track of the number of steps taken and the distance traveled. based on the information in the table, complete the statement about whether there is a proportional relationship between the two quantities.

number of steps	distance in kilometers
2,852	3
4,845	5.1

there select choice a proportional relationship because there select choice a constant of proportionality.
(lesso select choice
is
is not

Explanation:

Step1: Check Proportionality

To determine proportionality, we check if \(\frac{\text{Number of Steps}}{\text{Distance}}\) is constant.
For first row: \(\frac{950}{1} = 950\)
For second row: \(\frac{2852}{3} \approx 950.67\) (not equal to 950)
For third row: \(\frac{4845}{5.1} \approx 950\) (close, but second row differs slightly, but actually, let's recalculate second row: \(950\times3 = 2850\), but table has 2852. So the ratios are not exactly constant. Wait, wait, maybe I miscalculated. Wait, \(950\times3 = 2850\), but the table has 2852. So the first ratio is 950, second is \(2852/3 \approx 950.666\), third is \(4845/5.1 = 950\) (since \(5.1\times950 = 4845\)). Wait, maybe the second row is a typo? No, the problem is as given. Wait, \(950\times3 = 2850\), but table has 2852. So the ratio for second row is \(2852/3 \approx 950.67\), which is not equal to 950. So the constant of proportionality (ratio) is not the same for all rows. Wait, but third row: \(5.1\times950 = 4845\), which matches. So first and third rows have ratio 950, second has ~950.67. So there is not a constant of proportionality (since the ratio isn't exactly the same for all). Wait, but maybe the second row is a mistake? No, the problem is to check. So the key is: in a proportional relationship, \(\text{Number of Steps} = k \times \text{Distance}\), where \(k\) is constant. So \(k = \text{Number of Steps}/\text{Distance}\) must be same for all.

First: \(k = 950/1 = 950\)
Second: \(k = 2852/3 \approx 950.67\) (not 950)
Third: \(k = 4845/5.1 = 950\)

Since \(k\) is not constant (second row differs), there is no constant of proportionality, so the relationship is not proportional.

Step2: Conclude

Since the ratio (constant of proportionality) is not the same for all pairs, there is no proportional relationship.

Answer:

There \(\boldsymbol{\text{is not}}\) a proportional relationship because there \(\boldsymbol{\text{is not}}\) a constant of proportionality.