Answer:
Slope, M = 5 and this means that profit is five (5) times every unit change in the quantity of candies.
Step-by-step explanation:
Let the equation below represent the Profit and number of candies relationship:
π (x) = Mx +c--------------------------------------------------------------- (1)
Where π = Profit
x = Number of candies sold
M = Slope of the linear relationship/ equation
C = The profit intercept of the linear equation or relationship
From the question two different coordinates of profit and the number of candies where given: (π₁ ,x₁) and (π₂ ,x₂)
First coordinate (π₁ ,x₁) = ($30 , 4)
Second coordinate (π₂ ,x₂) = ($70, 12)
These can be substituted into equation (1) and (2) to calculate the for M & C
Substituting the first coordinate into (1) we have :
30 = 4M +C-----------------------------------------------------------------(2)
Substituting the second coordinate into (1) we have :
70 = 12M +C------------------------------------------------------------------(3)
Solving equation (2) and (3) simultaneously using elimination method, we have:
30 = 4M +C
70 = 12M +C
-40 = -8M
M = 5
Substituting the value of M into equation (3) we have:
70 = 12(5) +C
70 = 60 +C
C =10
Substituting the value of M and C into equation (1), we have the Linear relationship for profit and the number of candies sold as
π (x) = 5x + 10---------------------------------------------------------------- (4)
Slope = 5 and this means that profit changes five (5) times for every unit change in the quantity of candies.
