Question

Drag each object to show whether cost is proportional to area in the situation represented.

Answer 1

Answer:

see the explanation

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $k=\frac{y}{x}$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Verify each case

case 1) Sod that is quoted at a set price per square yard plus a labor fee

The Cost is NOT proportional to Area, because the line don't pass though the origin (the equation has an y-intercept equal to the labor fee)

case 2) Pavers that cost a set amount per square foot

The Cost is Proportional to Area

In this problem the constant of proportionality k is equal to the set amount per square feet

case 3) Hardwood flooring that cost $16 for every 2 square feet

The Cost is Proportional to Area

The constant of proportionality k is equal to

$k=\frac{y}{x}$ ----> $k=\frac{16}{2}=\ 8\ per square\ foot$

The linear equation is  $y=8x$

case 4) The given graph

Is a line that passes though the origin

so

The Cost is Proportional to Area

case 5) The given table

Find the constant of proportionality k for each ordered pair

If all values of k are the same, then the cost is proportional to area

For x=2, y=3,000 ->$k=\frac{y}{x}$ --> $k=\frac{3,000}{2}=1,500$

For x=4, y=4,000 ->$k=\frac{y}{x}$ --> $k=\frac{4,000}{4}=1,000$

For x=6, y=6,000 ->$k=\frac{y}{x}$ --> $k=\frac{6,000}{6}=1,000$

so

the values of k are different

therefore

The Cost is NOT proportional to Area

case 6) A concrete patio quoted at a bulk cost for 50 square feet

Not enough information