The cost to manufacture 5 toys is 17.50 ; The cost to manufacture 10 toys is $30. Construct a linear function in the form y = mx + b that represents the relationship between the number of toys that produced and the cost of producing them.

The correct answer is: y = 2.5x + 5

Let no of toys produced = x
Cost of producing 1 toy = y
It is given that cost to manufacture 5 toys is $17.50
i.e. x₁ = 5 and y₁ = 17.50
Also, the cost to manufacture 10 toys is $30.
i.e. x₂ = 10 and y₂ = 30.
Using two – point form, equation of the line is
(y – y₁) = m (x – x₁)  where  m =

m = 

 =  2.5
Now,  equation of the line is (y – y₁) = m (x – x₁) 
(y – 17.5) = 2.5 (x – 5)
y – 17.5 = 2.5x – 12.5
y = 2.5x - 12.5 + 17.5
y = 2.5x + 5
A linear function that represents the relationship between the number of toys that produced and the cost of producing them is y = 2.5x + 5