1. Welcome
to the presentation
on LINEAR EQUATION
Presented by
Nasim Khan
Assistant Professor
Department of Mathematics
Bangladesh University of
Business and Technology, Dhaka.

2. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
2
LINEAR EQUATION
TOPICS
Slope
Equation of line
Intercept
Slope-intercept form
Application of linear equation

3. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
3
Linear equation
Rule: If (x1,y1) and (x2 ,y2) be two points then
Slope , m = y2 – y1 / x2 – x1
Example:- If (12,- 5 ) and (3,6) are two points then
Slope, m = 6 – ( - 5 ) / 3 – 12
=11/(-8 )
Book- Bowen
Page- 25 to26
Same Problems: 9 to22

4. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
4
Linear equation
Rule: If (x1,y1) and (x2 ,y2) be two points then the
Line equation is
21
1
yy
yy
−
−
=
21
1
xx
xx
−
−

5. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
5
Linear equation
Example:- If (-2, -4)and (-1, 5) are two points
then, Find the equation of line.
Solution: We know ,The equation of a line is
=
21
1
yy
yy
−
−
21
1
xx
xx
−
−

6. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
6
Linear equation
⇒ =
⇒ -9(x+ 2)= -1(y+ 4)
⇒ - 9x – 18= - y – 4
⇒ - 9x + y = 14
Which is our required line equation.
Book- Bowen
Page- 36
Problem: 13 to 24
54
4
−−
+y
12
2
+−
+x

7. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
7
Linear equation
Rule: Slope-Intercept Form
y = m x + b
Where m is the slope and b is the y-
intercept
Example:-Write2y +3x =18 in slope-intercept
Form and state the value of the slope and
the y- intercept.

8. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
8
Linear equation
Solution: Given, the equationof the line is
2y + 3x=18
⇒ 2y = -3x +18
⇒ y = -3x/2 + 9
Which is our required form.
Therefore, slope of the line is -3/2 and y-intercept is 9 .
Book- Bowen
Page - 37
Problems: 47 to 50

9. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
9
Linear equation
Problem: If 5y - 2x = 30 is a linear equation
then find
(a) Write the slope-intercept form
(b) What is the slope of the line?
(c) What is the y-intercept?
(d) What is the x-intercept?
(e) Write the co-ordinate of the
points of the equation?

10. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
10
Linear equation
Solution: (a) Given, The line equation,
5y - 2x = 30 --- --- (1)
⇒ 5y = 2x + 30
⇒ y = 2x/5 + 6
Which is slope-intercept form.
(b) The slope of line is 2/5
(c) The y-intercept is 6
(d) Putting y = 0 in equation (1),then we have
5y – 2. 0 =30 ⇒ y = 30
So the x-intercept is 30.
(e) The co-ordinates of the points is (0,6) and (30 ,0)

11. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
11
Application of linear equation
 Cost function
 Average cost
 Marginal cost
What is cost function?
If x is the quantity produced of a certain goods by a firm at total cost c,
we can write the total cost function C = c (x)
There are two part of Total cost
(i) Fixed cost which is independent of x
(ii) Variable cost which is dependent of x
Therefore, Total cost = Variable cost + Fixed cost
⇒ TC = VC + FC

12. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
12
Application of linear equation
What is average cost?
If total cost (c) is represented as a function of output x,
the average cost (AC) represents the cost per unit of production.
i.e. Average cost = Total cost / Total quantity
= c / x
What is Marginal cost ?
Marginal cost represents the change in the total cost for each
additional unit of production.
i.e. Marginal cost = dc / dx
Marginal cost = Variable cost per unit = Slope

13. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
13
Application of linear equation
TOPICS
Revenue function
Break-even
Mark Up
Margin
Break- even Chart

14. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
14
Revenue function
Revenue is the amount of money derived from the sale
of a product and depends upon the price of a product
and the quantity of the product that is actually sold.
If q is the demand for the output of a firm at
price p, then total revenue (R) collected by the
firm is R(q) = pq
Revenue function:
R (q)=(Selling price per unit) (Number of units sold)
= p q
= Sales volumes (dollars)

15. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
15
Application of linear equation
Break-even: It means neither make a profit nor suffer a
loss. It’s simply means that revenue must equal costs.
So at break even, Revenue = Cost
i.e. Profit = 0.
Mark Up: It is the difference between the retail price and
the cost.
Therefore, Mark up = Retail price – cost

16. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
16
Application of linear equation
Example:- Suppose an stem costs $130 is price to sell at $200, Find Mark
up ?
Solution - We know, Mark up = Retail price –cost
= $(200 - 130) = $70
Mark up percentage on cost = 100% = 54%
Mark up percentage on retail price = 100% = 35%= Margin
Margin: Mark up / Retail price = 70/200 = 0.35 =35/100 = 35%
Margin 35% that means it is the markup percentage on retail price.
So 35% margin means (100- 35)% = 65% cost
130
70
200
70

17. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
17
Application of linear equation
BREAK-EVEN CHART
R&C
R
FCL
Q
NSO
L
T
M
I A
FC
VC
FC
VC
FC
TC
(Number of units)

18. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
18
Application of linear equation
CR & C
O
q
R
60,000
20,000
1,00,000
FCL
BEP
FC
Profit
Loss
( 20,000 , 100000 )
BREAK-EVEN CHART
BOOK- BOWEN, Page- 64 to 65, Problems- 13,14,15,16,29,30,31,32.

19. July 12, 2014 NK,Assistant Professor of
Mathematics,BUBT.
19
Home Work
Problems:
True/ False (1 to 12) & (19 to 28)
13,14,15,16,29,30,31,32
Page : 64 – 65
Book : Bowen