#### Answer

(a) The slope is 8.34 This represents the fact that every year of a child's life the dosage they are to receive increases by 8.34 mg.
(b)The dosage for a newborn is 8.34mg.

#### Work Step by Step

To find the slope of the equation, we will put the equation in slope-intercept form. That is,
(1) y = mx + b
The question specifies that in the equation
(2) c = .0417D(a+1)
c represents the child's dose of a drug in mg.
D represents the adult dose of a drug.
a represents the child's age.
The question gives that the adult dose is 200 mg, so we take equation (1) and substitute 200 for D.
(3) c = .0417(200)(a+1)
Multiplying through, we get
c = 8.34(a+1)
Distributing 8.34, we get
(4) c = 8.34a + 8.34
This is equation is now in the form y = mx + b.
Thus, the slope is 8.34
This means that each year the amount that a child needs grows by 8.34.
(b) To find the dosage for a new born, we plug in age a = 0. Thus, we take equation (4) and find that
c = 8.34(0) + 8.34
c= 8.34.
Thus, a new born should receive 8.34 mg.