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UNIT THREE
UNIVERSITY OF THE PEOPLE
1201-01: COLLEGE ALGEBRA
Task 1: Electricity Pricing
, 2
(i) Formulate the Linear Function
Let x be the number of units consumed and C(x) be the total cost.
C(x) = 0.78x + 50
Variables:
x: Independent variable representing electricity units.
C(x): Dependent variable representing the total monthly bill.
0.78: The variable rate or cost per unit (slope).
50: The fixed monthly service fee (y-intercept).
(ii) Average Rate of Change
The average rate of change for a linear function is constant and equal to the slope.
Calculation: (C(x2) - C(x1)) / (x2 - x1) = 0.78.
Impact: This means for every additional unit of electricity used, the consumer's bill increases by exactly
$0.78.
Task 2: City Planner Road Project
(i) Equation of the Road
Points: A(5, 7) and B(6, 5)
Slope (m) = (5 - 7) / (6 - 5) = -2
Equation: y - 7 = -2(x - 5)
Final Equation: y = -2x + 17
(ii) Traffic Flow Analysis
The slope of the road is -2.
(iii) Enhanced Traffic Safety
The road elevation decreases by 2 units for every 1 unit of horizontal distance covered from point A to B.
(iv) Alternate Routes Provision
Parallel route: y = -2x + 10 (same slope)
UNIT THREE
UNIVERSITY OF THE PEOPLE
1201-01: COLLEGE ALGEBRA
Task 1: Electricity Pricing
, 2
(i) Formulate the Linear Function
Let x be the number of units consumed and C(x) be the total cost.
C(x) = 0.78x + 50
Variables:
x: Independent variable representing electricity units.
C(x): Dependent variable representing the total monthly bill.
0.78: The variable rate or cost per unit (slope).
50: The fixed monthly service fee (y-intercept).
(ii) Average Rate of Change
The average rate of change for a linear function is constant and equal to the slope.
Calculation: (C(x2) - C(x1)) / (x2 - x1) = 0.78.
Impact: This means for every additional unit of electricity used, the consumer's bill increases by exactly
$0.78.
Task 2: City Planner Road Project
(i) Equation of the Road
Points: A(5, 7) and B(6, 5)
Slope (m) = (5 - 7) / (6 - 5) = -2
Equation: y - 7 = -2(x - 5)
Final Equation: y = -2x + 17
(ii) Traffic Flow Analysis
The slope of the road is -2.
(iii) Enhanced Traffic Safety
The road elevation decreases by 2 units for every 1 unit of horizontal distance covered from point A to B.
(iv) Alternate Routes Provision
Parallel route: y = -2x + 10 (same slope)
