PART I: MATHEMATICS OF LINEAR FUNCTIONS
Chapter 02
The Straight Line and Applications
Chapter overview
This chapter introduces linear functions, with applications. The straight line is one of the simplest
mathematical functions. In spite of its simplicity, the line serves as a model for numerous
economic/business situations: demand, supply, cost, revenue, consumption, and savings.
Topics covered in this chapter:
PART I: Mathematics of Linear function (Straight Line)
Describe the slope and intercept of a line verbally and illustrate these ideas graphically.
Explain the equation of a line as the formula that describes the relationship between the x and
y co-ordinate at every point on the line.
Explain how the intercept and slope of a line are used to give in the formula/equation of a line
Deduce the equation of a line when given
(a) slope and intercept
(b) slope and one point
(c) two points.
Write down the slope and intercept of a line from its equation.
Plot a line when given
(a) slope and intercept
(b) its equation in any format
PART II: The Applications of Linear function (Straight Line)
Demand; Supply; price
Cost functions
Total revenue functions
Profit
Price elasticity of demand and supply.
PREPARED BY: S. SRITHARAN 1
, PART I: MATHEMATICS OF LINEAR FUNCTIONS
PART I: Mathematics of Linear Functions (Straight Line)
Learning Outcomes:
At the end of this section you should be able to:
• Define the slope and intercept of a straight line and plot its graph
• Understand what 'the equation of a line' means
• Plot any straight line given the equation in the form y = mx + c or ax + by + d = 0
• Calculate the slope of a line given two points on the line
• Determine the equation of a line given slope and any point on the line
• Determine the equation of a line given any two points on the line
2.1 The straight line: Slope, Intercept and Graph
Introductory background on graphs: Cartesian coordinate system
Figure 2.1 shows points on Cartesian
coordinate system. In this, the
horizontal axis, x, and the vertical axis,
y, which intersect at the origin where x
= 0 and y = 0. Any point can be plotted
on this graph if the coordinates, (x, y)
are known; that is, the x-coordinate
(with sign) is stated first and measured
along the horizontal axis, followed by
its y-coordinate (with sign) measured
along the vertical axis. The points (2,
2), (1, 1), (2, -2), (- 4, -3), (-3, 2)
and (0, 0) are plotted in Figure 2.1.
Figure 2.1: Plotting points on a graph
Define a straight line
A line is uniquely defined by both slope and vertical intercept.
• Slope is usually represented by the symbol m
• Vertical intercept is usually represented by the symbol c.
PREPARED BY: S. SRITHARAN 2
, PART I: MATHEMATICS OF LINEAR FUNCTIONS
Slope
The slope of a line is simply the 'slant' of the line. The slope is negative if the line is falling from left
to right and the slope is positive if the line is rising from left to right, (see Figure 2.2).
Each line has a different slope and a
different intercept.
Note:
The slope of a horizontal line is
zero.
A vertical line has an infinite
slope.
Figure 2.2: Lines with different slopes and different intercepts
Measuring the slope of a line:
The slope of a straight line is the change in height (denoted by y ) divided by the corresponding
increase in horizontal distance (denoted as x ).
Change in height Change in y y
Slope m
Change in dis tan ce Change in x x
Describing the slope of a line:
“The number of units by which y changes when x increases by 1 unit”
Or in other words
“The change in y per unit increases in x”
Figure 2.3 shows how the slope of a line is measured.
PREPARED BY: S. SRITHARAN 3
Chapter 02
The Straight Line and Applications
Chapter overview
This chapter introduces linear functions, with applications. The straight line is one of the simplest
mathematical functions. In spite of its simplicity, the line serves as a model for numerous
economic/business situations: demand, supply, cost, revenue, consumption, and savings.
Topics covered in this chapter:
PART I: Mathematics of Linear function (Straight Line)
Describe the slope and intercept of a line verbally and illustrate these ideas graphically.
Explain the equation of a line as the formula that describes the relationship between the x and
y co-ordinate at every point on the line.
Explain how the intercept and slope of a line are used to give in the formula/equation of a line
Deduce the equation of a line when given
(a) slope and intercept
(b) slope and one point
(c) two points.
Write down the slope and intercept of a line from its equation.
Plot a line when given
(a) slope and intercept
(b) its equation in any format
PART II: The Applications of Linear function (Straight Line)
Demand; Supply; price
Cost functions
Total revenue functions
Profit
Price elasticity of demand and supply.
PREPARED BY: S. SRITHARAN 1
, PART I: MATHEMATICS OF LINEAR FUNCTIONS
PART I: Mathematics of Linear Functions (Straight Line)
Learning Outcomes:
At the end of this section you should be able to:
• Define the slope and intercept of a straight line and plot its graph
• Understand what 'the equation of a line' means
• Plot any straight line given the equation in the form y = mx + c or ax + by + d = 0
• Calculate the slope of a line given two points on the line
• Determine the equation of a line given slope and any point on the line
• Determine the equation of a line given any two points on the line
2.1 The straight line: Slope, Intercept and Graph
Introductory background on graphs: Cartesian coordinate system
Figure 2.1 shows points on Cartesian
coordinate system. In this, the
horizontal axis, x, and the vertical axis,
y, which intersect at the origin where x
= 0 and y = 0. Any point can be plotted
on this graph if the coordinates, (x, y)
are known; that is, the x-coordinate
(with sign) is stated first and measured
along the horizontal axis, followed by
its y-coordinate (with sign) measured
along the vertical axis. The points (2,
2), (1, 1), (2, -2), (- 4, -3), (-3, 2)
and (0, 0) are plotted in Figure 2.1.
Figure 2.1: Plotting points on a graph
Define a straight line
A line is uniquely defined by both slope and vertical intercept.
• Slope is usually represented by the symbol m
• Vertical intercept is usually represented by the symbol c.
PREPARED BY: S. SRITHARAN 2
, PART I: MATHEMATICS OF LINEAR FUNCTIONS
Slope
The slope of a line is simply the 'slant' of the line. The slope is negative if the line is falling from left
to right and the slope is positive if the line is rising from left to right, (see Figure 2.2).
Each line has a different slope and a
different intercept.
Note:
The slope of a horizontal line is
zero.
A vertical line has an infinite
slope.
Figure 2.2: Lines with different slopes and different intercepts
Measuring the slope of a line:
The slope of a straight line is the change in height (denoted by y ) divided by the corresponding
increase in horizontal distance (denoted as x ).
Change in height Change in y y
Slope m
Change in dis tan ce Change in x x
Describing the slope of a line:
“The number of units by which y changes when x increases by 1 unit”
Or in other words
“The change in y per unit increases in x”
Figure 2.3 shows how the slope of a line is measured.
PREPARED BY: S. SRITHARAN 3
