G8 Math Q2- Week 5- Problems Involving Linear Function.ppt

G8 Math Q2- Week 5- Problems Involving Linear Function.ppt

1. LINEAR
FUNCTIONS

2. Linear Functions
Linear functions exhibit many real-life situations.
It is widely used in economics, science,
engineering and many everyday applications.
Businesses allow them to determine the
increase or decrease of sales. Doctors can help
them in determining the amount of dosage of a
certain medicine for a specific age. Linear
functions help us model any real-world
3
phenomena.

3. REVIEW OF FORMULAS
Formula for Slopem
y
2
y
1
x
2
x
1
AxByC
ymxb
yy
1mxx
1
Standard Form
Slope-intercept Form
Point-Slope Form
*where A>0 and A, B, C are integers

4. Find the slope of a line through
points (3, 4) and (-1, 6).
m
64
13

2
4

1
2

5. Change into
standard form.
y
3
4
x2
4y4
3
4
x42
3x4y8
3x4y8

6. Change into slope-intercept
form and identify the slope and y-
intercept.
3x5y15
5y3x15
5y
5

3x
5

15
5
3
3
5
y x 
3
5
5
m andb 

7. Write an equation for the line that
passes through (-2, 5) and (1, 7):
Find the slope:m
75
12

2
3
Use point-
slope form:
y5
2
3
x2

8. x-intercepts and y-intercepts
The intercept is the point(s)
where the graph crosses the axis.
To find an intercept, set the other
variable equal to zero.
3x5y15
3x5015
3x15
x5
5,0 is the
-interceptx

9. Horizontal Lines
 Slope is zero.
 Equation form is y = #.
Write an equation of a line and graph it
with zero slope and y-intercept of -2.
y = -2
Write an equation of a line and graph it
that passes through (2, 4) and (-3, 4).
y = 4

10. Vertical Lines
 Slope is undefined.
 Equation form is x = #.
Write an equation of a line and graph it
with undefined slope and passes
through (1, 0).
x = 1
Write an equation of a line that passes
through (3, 5) and (3, -2).
x = 3

11. Graphing Lines
*You need at least 2 points to
graph a line.
Using x and y intercepts:
•Find the x and y intercepts
•Plot the points
•Draw your line

12. Graph using x and y intercepts
2x – 3y = -12
x-intercept
2x = -12
x = -6
(-6, 0)
y-intercept
-3y = -12
y = 4
(0, 4)
6
4
2
-2
-10 -5
B: (0, 4)
A: (-6, 0)
B
A

13. Graph using x and y intercepts
6x + 9y = 18
x-intercept
6x = 18
x = 3
(3, 0)
y-intercept
9y = 18
y = 2
(0, 2)
4
2
-2
5
D: (0, 2)
C: (3, 0)
D
C

14. Graphing Lines
Using slope-intercept form y = mx + b:
•Change the equation to y = mx + b.
•Plot the y-intercept.
•Use the numerator of the slope to count the
corresponding number of spaces up/down.
•Use the denominator of the slope to count the
corresponding number of spaces left/right.
•Draw your line.

15. Graph using slope-intercept form
y = -4x + 1:
Slope
m = -4 = -4
1
y-intercept
(0, 1)
4
2
-2
-4
5
F: (1, -3)
E: (0, 1)
F
E

16. Graph using slope-intercept form
3x - 4y = 8
Slope
m = 3
4
y-intercept
(0, -2)
y = 3x - 2
4
4
2
-2
-4
5
H: (0, -2)
G: (4, 1)
G
H

17. Parallel Lines
**Parallel lines have the same slopes.
•Find the slope of the original line.
•Use that slope to graph your new line
and to write the equation of your new
line.

18. Graph a line parallel to the given
line and through point (0, -1):
2
-2
-4
5
3
5
Slope = 3
5

19. Write the equation of a line parallel to
2x – 4y = 8 and containing (-1, 4):
– 4y = - 2x + 8
y = 1x - 2
2

Slope =1
2
y - 4 = 1(x + 1)
2
yy
1mxx
1

20. Perpendicular Lines
**Perpendicular lines have the
opposite reciprocal slopes.
•Find the slope of the original line.
•Change the sign and invert the
numerator and denominator
of the slope.
•Use that slope to graph your new
line and to write the equation
of your new line.

21. 4
2
-2
5
-3
4
Graph a line perpendicular to the
given line and through point (1, 0):
Slope =-3
4
Perpendicular
Slope=4
3

22. Write the equation of a line
perpendicular to
y = -2x + 3 and containing (3, 7):
Original Slope= -2
y - 7 = 1(x - 3)
2
yy
1mxx
1
Perpendicular
Slope =1
2

23. Slope= 3
4
y - 4 = -4(x + 1)
3
yy
1mxx
1
Perpendicular
Slope = -4
3
Write the equation of a line
perpendicular to
3x – 4y = 8 and containing (-1, 4):
-4y = -3x + 8
3
2
4
 y x

24. Problem 1
1. How many wallets must be sold to
have a profit of Php 30?
2. How much profit will Mikaela make if
2 wallets were sold?
3. Express the functionin terms of .

25. Problem 1
1. How many wallets must be sold to
have a profit of Php 30?
5 wallets must be sold
to
have a Php 30
profit.

26. Problem 1
2. How much profit will Mikaela make if
2 wallets were sold?
Mikaella will
make a profit of
Php 15
if 2 wallets were
sold.

27. Problem 1
3. Express the functionin
terms of .
(0, 5) and 4, 25
2 − 1
− 1 =
2 − 1
− 5 = 25 − 5
4 − 0
− 5 = 20
4
− 5 = 5
= 5 + 5
5 −= −5
−
− 0
1
Choose any two points from the graph.
Use the Two-Point form in solving for the
linear function.
Substitution
Simplify
Simplify
Slope-intercept form
Standard form

28. Problem 2
The Shoe Factory formulated an
equation ( ) = 500 + 70 which
represents the number of
manufactured shoes ( ) and the cost
of manufacture ( ).
a. What is the cost of manufacturing 40
shoes?
b. If the cost of manufacturing shoes is
Php 7,570, how many shoes are
manufactured?
c. What is the cost of manufacturing 10
8
shoes?

29. Problem 2
The Shoe Factory formulated an equation( ) = 500+ 70 which
represents the number of manufactured shoes ( ) and the cost of
manufacture ( ).
a. What is the cost of manufacturing 40 shoes?
Answer:
Let= number of manufactured shoes = 40
= cost of manufacture shoes = 500 + 70
40 = 500 40 + 70
Equation: = 500 + 70
40 = 20,000
+ 70
= ,
Therefore, the cost of manufacturing 40 shoes is,
.
9

30. Problem 2
The Shoe Factory formulated an equation( ) = 500+ 70 which
represents the number of manufactured shoes ( ) and the cost of
manufacture ( ).
b. If the cost of manufacturing shoes is Php 7,570, how many shoes are
Answer:manufactured?
( ) = 7,570
= 500 + 70
7,570 = 500 + 70
7,570 − 70 = 500
500= 7,500
=
Therefore, the cost of manufacturing 15 shoes is Php 7,570.
10

31. Problem 2
The Shoe Factory formulated an equation( ) = 500+ 70 which
represents the number of manufactured shoes ( ) and the cost of
manufacture ( ).
c. What is the cost of manufacturing 10 shoes?
Answer:
= 10
= 500 + 70
10 = 500 10 + 70
10 = 5,000 + 70
= ,
Therefore, the cost of
manufacturing 10 shoes is
,.
11

32. Problem 3
Cassandrea decides to start solving math problems in
preparation of the upcoming MTAP. She started
answering 5 problems in day 1, 9 problems in day 2,
13 problems in day 3 and so on.
a. Present your answer in a table until the 6th day.
b. Write a linear function in slope-intercept form to
represent the given problem.
c. How many problems Cassandrea need to
answer on the 10th day?
d. In what day does Cassandrea12need to solve 33