Organic Name Reactions for the students and aspirants of Chemistry12th.pptx
Β
Math 8 - Linear Functions
1. MATHEMATICS 8
Quarter 2 Week 4
Linear
Functions
MR. CARLO JUSTINO J. LUNA
MALABANIAS INTEGRATED SCHOOL
Angeles City
2. Learning Competency
2
β Graphs and illustrates a linear function and
its (a) domain; (b) range; (c) table of values;
(d) intercepts; and (e) slope (M8AL-IId-1)
3. Linear Function
A linear function is a function that can be written in the
form
π π = ππ + π
β where π and π are real numbers
β where π tells us the slope of a line and π tells us
where the graph crosses the π¦-axis.
3
4. Linear Function
π π = ππ + π
A linear function is a function whose graph is a straight
line. Its equation can be written in the form π = ππ +
π, where π₯ and π¦ are used for the independent and
dependent variables, respectively, π β 0.
4
5. Linear Function
π π = ππ + π
π = ππ + π
π = π π
π(π) or π(π)
5
β π(π₯) means βthe value of π at π₯β
β letters other than π such as πΊ and π», or π
and β can also be used.
6. 6
Linear Functionas an Equation
Which of the following function is linear?
π = ππ + π
π π = ππ + π
1. π¦ = 8π₯ β 5
2. π¦ = β
π₯
3
+ 2
3. π¦ = π₯
4. π¦ =
2
π₯
+ 7
5. π¦ = π₯2
β 3
Linear Function. It is in the form π¦ = ππ₯ + π, where π = 8 and
π = β5
Linear Function. By rewriting the equation, we can have π¦ =
β
1
3
π₯ + 2 where π = β
1
3
and π = 2.
Linear Function. By rewriting the equation, we can have π¦ =
π₯ + 0 where π = 1 and π = 0.
Not a Linear Function. It cannot be expressed in the form π¦ =
ππ₯ + π because π₯ is in the denominator.
Not a Linear Function. The degree of the equation is on the
second degree.
7. 7
A linear function can alsobe describedusing its
graph.
Letβs determine the values of the function π if π π₯ = 2x + 1 at π₯ =
β 2, β1, 0, 1, and 2, and see if it will illustrate a straight line.
SOLUTION:
1. π π₯ = 2π₯ + 1
π β2 = 2 β2 + 1
π β2 = β4 + 1
π βπ = βπ
Ordered pair: (βπ, βπ)
π π(π)
βπ βπ
REMEMBER: Note that an ordered pair (π₯, π¦) can be
written as (π₯, π π₯ ) for any function in π π₯ notation.
8. 8
A linear function can alsobe describedusing its
graph.
Letβs determine the values of the function π if π π₯ = 2x + 1 at π₯ =
β 2, β1, 0, 1, and 2, and see if it will illustrate a straight line.
SOLUTION:
2. π π₯ = 2π₯ + 1
π β1 = 2 β1 + 1
π β1 = β2 + 1
π βπ = βπ
Ordered pair: (βπ, βπ)
π π(π)
βπ βπ
βπ βπ
9. 9
A linear function can alsobe describedusing its
graph.
Letβs determine the values of the function π if π π₯ = 2x + 1 at π₯ =
β 2, β1, 0, 1, and 2, and see if it will illustrate a straight line.
SOLUTION:
3. π π₯ = 2π₯ + 1
π 0 = 2 0 + 1
π 0 = 0 + 1
π π = π
Ordered pair: (π, π)
π π(π)
βπ βπ
βπ βπ
π π
10. 10
A linear function can alsobe describedusing its
graph.
Letβs determine the values of the function π if π π₯ = 2x + 1 at π₯ =
β 2, β1, 0, 1, and 2, and see if it will illustrate a straight line.
SOLUTION:
4. π π₯ = 2π₯ + 1
π 1 = 2 1 + 1
π 1 = 2 + 1
π π = π
Ordered pair: (π, π)
π π(π)
βπ βπ
βπ βπ
π π
π π
11. 11
A linear function can alsobe describedusing its
graph.
Letβs determine the values of the function π if π π₯ = 2x + 1 at π₯ =
β 2, β1, 0, 1, and 2, and see if it will illustrate a straight line.
SOLUTION:
5. π π₯ = 2π₯ + 1
π 2 = 2 2 + 1
π 2 = 4 + 1
π π = π
Ordered pair: (π, π)
π π(π)
βπ βπ
βπ βπ
π π
π π
π π
12. 12
A linear function can alsobe describedusing its
graph.
Letβs determine the values of the function π if
π π₯ = 2x + 1 at π₯ = β2, β1, 0, 1, and 2, and see if
it will illustrate a straight line.
π π(π)
βπ βπ
βπ βπ
π π
π π
π π
13. 13
A linear function can alsobe illustratedusinga table
of values.
We can do this by looking at the first difference of the π₯-
coordinates and π¦-coordinates.
π βπ βπ π π π
π(π) β3 β1 1 3 5
+π +π +π +π
+π +π +π +π
Since both quantities change by constant
amounts, this means that the relationship
between the quantities is linear.
14. 14
A linear function can alsobe illustratedusinga table
of values.
π π π π π π
π(π) 3 6 9 12 15
+π +π +π +π
+π +π +π +π
Since the π₯-coordinates and the π¦-coordinates
increase by constant amounts, this table of values
illustrates a linear function.
15. 15
A linear function can alsobe illustratedusinga table
of values.
π βπ βπ βπ π π
π(π) 2 3 5 8 12
+π +π +π +π
+π +π +π +π
Since the π₯-coordinates and the π¦-coordinates do
not increase by constant amounts, this table of
values does not illustrate a linear function.
16. 16
A linear function can alsobe illustratedusinga table
of values.
π π ππ ππ ππ ππ
π(π) 25 50 75 100 125
+π +π +π +π
+ππ +ππ +ππ +ππ
Since the π₯-coordinates and the π¦-coordinates
increase by constant amounts, this table of values
illustrates a linear function.
17. MATHEMATICS 8
Quarter 2 Week 4
Thank
you!
MR. CARLO JUSTINO J. LUNA
MALABANIAS INTEGRATED SCHOOL
Angeles City