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.
