reggie and his friends set out to sea on their annual fishing trip. this table shows the relationship…

reggie and his friends set out to sea on their annual fishing trip. this table shows the relationship between the time (in hours) reggie and his friends spend sailing, x, and their distance from shore (in miles), y.\n|x (hours)|y (miles)|\n|----|----|\n|2.8|42|\n|5|75|\n|7|105|\n|7.2|108|\naccording to the values in the table, do x and y have a proportional relationship?\nyes\nno\nwrite an equation for the relationship between x and y. simplify any fractions.\ny =

reggie and his friends set out to sea on their annual fishing trip. this table shows the relationship between the time (in hours) reggie and his friends spend sailing, x, and their distance from shore (in miles), y.\n|x (hours)|y (miles)|\n|----|----|\n|2.8|42|\n|5|75|\n|7|105|\n|7.2|108|\naccording to the values in the table, do x and y have a proportional relationship?\nyes\nno\nwrite an equation for the relationship between x and y. simplify any fractions.\ny =

Answer

Explanation:

Step1: Calculate the ratio for each pair

For the first pair $(x = 2.8,y = 42)$, the ratio $\frac{y}{x}=\frac{42}{2.8}=15$. For the second pair $(x = 5,y = 75)$, the ratio $\frac{y}{x}=\frac{75}{5}=15$. For the third pair $(x = 7,y = 105)$, the ratio $\frac{y}{x}=\frac{105}{7}=15$. For the fourth pair $(x = 7.2,y = 108)$, the ratio $\frac{y}{x}=\frac{108}{7.2}=15$.

Step2: Determine the relationship

Since the ratio $\frac{y}{x}$ is constant ($15$) for all pairs, $x$ and $y$ have a proportional relationship.

Step3: Write the equation

The equation for a proportional relationship is $y=kx$, where $k$ is the constant of proportionality. Since $k = 15$, the equation is $y = 15x$.

Answer:

$y = 15x$