A carpet installer charges a flat rate of $40, plus $1.50 per square foot for labor. So, the total cost for labor depends on the amount of carpet
installed.

A carpet installer charges a flat rate of $40, plus $1.50 per square foot for labor. So, the total cost for labor depends on the amount of carpet installed. The relationship between the total cost for labor and the amount of carpet installed is . The domain of the relation is x ≥ . The range of the relation is y ≥

Part 1)

Let

x ----> square feet of carpet installed

y ---> the total cost for labor

we know that

The linear equation in slope intercept form is equal to

[tex]y=mx+b[/tex]

In this problem we have

The slope is equal to

[tex]m=\$1.50\ per\ square\ foot[/tex]

The y-intercept or initial value is

[tex]b=\$40[/tex]

substitute

[tex]y=1.50x+40[/tex]

This is a non proportional relationship between the variables x and y (because the line don't pass through the origin)

Part 2) Find the domain of the relation

Remember that

The domain of a function is the set of all possible values of x

x ----> square feet of carpet installed

so

The domain is the amount of carpet installed

[tex]x\geq 0[/tex]

The domain is the interval [0,∞)

Part 3) Find the range of the relation

Remember that

The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.

y ---> the total cost for labor

so

The range is the total cost for labor

For x=0

The value of y=$40

The range is the interval [40,∞)

[tex]y\geq 40[/tex]