212k views
0 votes
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.

User Gizel
by
8.7k points

1 Answer

2 votes

Answer

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

Step-by-step 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}}=(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 = }(4-0)/(2-0)

Hope this Helps!!!

User Joseph Stine
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories