The correct choices are:
The slope is positive.
Each additional hat produced results in a cost increase of $0.60.
Before producing any hats, the manufacturing costs are about $100.00.
Explanation
We know the slope is positive, since the data increases every time.
We find the slope using the formula
m=(y₂-y₁)/(x₂-x₁)
m=(111-105)/(20-10) = 6/10 = 0.6
This means the slope is $0.60. This means that each additional hat manufactured results in an additional cost of $0.60.
We can write an equation to use in order to find the cost associated with any number of hats produced. We will use point-slope form:
y-y₁=m(x-x₁)
y-105=0.6(x-10)
Using the distributive property,
y-105=0.6*x-0.6*10
y-105=0.6x-6
Add 105 to both sides:
y-105+105=0.6x-6+105
y=0.6x+99
To find the cost before producing any hats, we use 0 for x:
y=0.6(0)+99=0+99=99
This means the manufacturing cost before any hats are produced is almost $100.
