Questions: relationship between the time (in hours) spent sailing, (x), and the distance (in miles) that the Parker family traveled from shore, (y). (y=6 x) (k=b) This table shows the proportional relationship between the number of hours Josiah worked, (x), and the number of dollars he earned, (y). (x) 2 4 6 10 (y) 30 60 90 150 (k=)

Solution Steps

The table shows the proportional relationship between the number of hours Josiah worked (x) and the number of dollars he earned (y). The values given are:

• For 2 hours, he earned $30.
• For 4 hours, he earned $60.
• For 6 hours, he earned $90.
• For 10 hours, he earned $150.

The constant of proportionality (k) can be found using the formula \( k = \frac{y}{x} \). Using the values from the table:

• For 2 hours: \( k = \frac{30}{2} = 15 \)
• For 4 hours: \( k = \frac{60}{4} = 15 \)
• For 6 hours: \( k = \frac{90}{6} = 15 \)
• For 10 hours: \( k = \frac{150}{10} = 15 \)

Since the constant of proportionality (k) is the same (15) for all given values, the relationship is consistent and proportional.

Final Answer