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 [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
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
[tex]k=\frac{y}{x}[/tex] ----> [tex]k=\frac{16}{2}=\$8\ per square\ foot[/tex]
The linear equation is [tex]y=8x[/tex]
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 ->[tex]k=\frac{y}{x}[/tex] --> [tex]k=\frac{3,000}{2}=1,500[/tex]
For x=4, y=4,000 ->[tex]k=\frac{y}{x}[/tex] --> [tex]k=\frac{4,000}{4}=1,000[/tex]
For x=6, y=6,000 ->[tex]k=\frac{y}{x}[/tex] --> [tex]k=\frac{6,000}{6}=1,000[/tex]
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
