Question

After a shipwreck, Harry is stranded on a desert Island. He needs to build a shelter, so he makes an axe using materials from the wreckage and starts cutting down trees. There is a proportional relationship between the number of days Harry is stranded on the Island, x, and the total number of trees he cuts down, y.

Answer 1

Answer

The constant of proportionality = 2 trees cut down per day spent on the island.

Explanation

The total number of trees he cut down is y

The number of days Harry is stranded on the island is x

The fact that these two quantities are directly proportional to each other is represented as

y ∝ x

If we introduce the constant of proportionality, we will write it as

y = kx

To now obtain the constant of proportionality, we will use the graph of the relationship between x and y. The costant of proportionality is the same as the slope of the graph

For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

$Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}$

For this question, the two points are

(x₁, y₁) and (x₂, y₂) are (0, 0) and (2, 4)

$\text{Slope = }\frac{4-0}{2-0}$

Hope this Helps!!!