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Read the description of a proportional relationship. $\newline$ After a shipwreck, Vivian is stranded on a desert island. She needs to build a shelter, so she makes an axe using materials from the wreckage and starts cutting down trees. There is a proportional relationship between the number of days Vivian is stranded on the island, $x$ , and the total number of trees she cuts down, $y$ . $\newline$ In her first $2$ days on the island, Vivian cuts down a total of $6$ trees. Write the equation for the relationship between $x$ and $y$ . $\newline$ $y = \_$

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Write and solve equations for proportional relationships

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Q. Read the description of a proportional relationship.

\newline

After a shipwreck, Vivian is stranded on a desert island. She needs to build a shelter, so she makes an axe using materials from the wreckage and starts cutting down trees. There is a proportional relationship between the number of days Vivian is stranded on the island,

x

, and the total number of trees she cuts down,

y

.

\newline

In her first

2

days on the island, Vivian cuts down a total of

6

trees. Write the equation for the relationship between

x

and

y

.

\newline

y = \_

Determine Constant of Proportionality: First, we need to determine the constant of proportionality, $k$ , which is the number of trees cut down per day. Since Vivian cuts down $6$ trees in $2$ days, we calculate $k$ by dividing the total number of trees by the number of days.
Write Equation for Relationship: Next, we use the constant of proportionality to write the equation that describes the relationship between the number of days Vivian is stranded ( $x$ ) and the total number of trees she cuts down ( $y$ ). The equation is $y = kx$ .

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