authentic learning in mathrmatics

1. Mathematics : grade11
Functions : linear equations
X.C NGWENYA
201007180

2. Lesson outcome
 Identify linear equations and functions.
 Write linear equations in standard form
and graph them.
You will learn to
calculate the
y-intercept
 x-intercept

3. INTRODUCTION
• A linear equation is an algebraic equation in
which each term is either a constant or the
product of a constant and (the first power of)
a single variable.
• Linear equations can have one or more
variables. Linear equations occur with great
regularity in applied mathematics. Linear
equations do not include exponents.

4. Linear Equations
y
6
Spounge has 4 hours after dinner to study and do
homework. He has brought home algebra 2 4
and chemistry.
x+ y =4
2
If he spends x hours on algebra and y
hours on chemistry, a portion of the graph
0 x
of the equation x + y = 4 can be used to
relate how much time she spends on each.
-2
-2 2 4 6
0
An equation such as x + y = 4 is called a linear equation.

5. Linear Equations
A linear equation has no operations other than:
addition subtraction multiplication of a variable by a constant
________, ___________, and ____________________________________.
The variables may not be multiplied together or appear in a ____________.
denominator
A linear equation does not contain variables with exponents other than __.
1
The graph of a linear equation is always a ____.
line
Linear Equations Not Linear Equations
5x − 3 y = 7 7 a + 4b 2 = −8
x=9 y = x+5
6 s = −3t − 15 x + xy = 1
1 1
y= x y=
2 x

6. Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and b
are real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x

7. Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and b
are real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x Yes!

8. Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and b
are real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x Yes!
It can be written as f(x) = – 5x + 10
m = – 5, b = 10
b) g(x) = x4 – 5

9. Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and b
are real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x Yes!
It can be written as f(x) = – 5x + 10
m = – 5, b = 10
b) g(x) = x4 – 5 No!

10. Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and b
are real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x Yes!
It can be written as f(x) = – 5x + 10
m = – 5, b = 10
b) g(x) = x4 – 5 No!
x has an exponent other than 1.

11. Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and b
are real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x Yes!
It can be written as f(x) = – 5x + 10
m = – 5, b = 10
b) g(x) = x4 – 5 No!
x has an exponent other than 1.
c) h(x, y) = 2xy

12. Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and b
are real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x Yes!
It can be written as f(x) = – 5x + 10
m = – 5, b = 10
b) g(x) = x4 – 5 No!
x has an exponent other than 1.
c) h(x, y) = 2xy No!

13. Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and b
are real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x Yes!
It can be written as f(x) = – 5x + 10
m = – 5, b = 10
b) g(x) = x4 – 5 No!
x has an exponent other than 1.
c) h(x, y) = 2xy No!
Two variables are multiplied together.

14. Example
Find the x-intercept and the y-intercept of the graph of the equation.
Then graph the equation.
5 x + 3 y = 15
y
x

15. Linear Equations
Find the x-intercept and the y-intercept of the graph of the equation.
Then graph the equation.
5 x + 3 y = 15
The x-intercept is the value of x when y = 0. y
5 x + 3(0) = 15
x

16. Linear Equations
Find the x-intercept and the y-intercept of the graph of the equation.
Then graph the equation.
5 x + 3 y = 15
The x-intercept is the value of x when y = 0. y
5 x + 3(0) = 15
5 x = 15
x

17. Linear Equations
Find the x-intercept and the y-intercept of the graph of the equation.
Then graph the equation.
5 x + 3 y = 15
The x-intercept is the value of x when y = 0. y
5 x + 3(0) = 15
5 x = 15
x
x=3 (3, 0)

18. Linear Equations
Find the x-intercept and the y-intercept of the graph of the equation.
Then graph the equation.
5 x + 3 y = 15
The x-intercept is the value of x when y = 0. y
5 x + 3(0) = 15
5 x = 15
x
x=3 (3, 0)
The y-intercept is the value of y when x = 0.
5(0) + 3 y = 15

19. Linear Equations
Find the x-intercept and the y-intercept of the graph of the equation.
Then graph the equation.
5 x + 3 y = 15
The x-intercept is the value of x when y = 0. y
(0, 5)
5 x + 3(0) = 15
5 x = 15
x
x=3 (3, 0)
The y-intercept is the value of y when x = 0.
5(0) + 3 y = 15
3 y = 15
y =5

20. Linear Equations
Find the x-intercept and the y-intercept of the graph of the equation.
Then graph the equation.
5 x + 3 y = 15
The x-intercept is the value of x when y = 0. y
(0, 5)
5 x + 3(0) = 15
5 x = 15
x
x=3 (3, 0)
The y-intercept is the value of y when x = 0.
5(0) + 3 y = 15
3 y = 15
y =5

21. Linear Equations
Find the x-intercept and the y-intercept of the graph of the equation.
Then graph the equation.
5 x + 3 y = 15
The x-intercept is the value of x when y = 0. y
5 x + 3(0) = 15
5 x = 15
x
x=3 (3, 0)
The y-intercept is the value of y when x = 0.
5(0) + 3 y = 15
3 y = 15

22. Linear Equations
Find the x-intercept and the y-intercept of the graph of the equation.
Then graph the equation.
5 x + 3 y = 15
The x-intercept is the value of x when y = 0. y
(0, 5)
5 x + 3(0) = 15
5 x = 15
x
x=3 (3, 0)
The y-intercept is the value of y when x = 0.
5(0) + 3 y = 15
3 y = 15
y =5

23. Find the x-intercept and the y-intercept of the graph of the equation.
Then graph the equation.
5 x + 3 y = 15
The x-intercept is the value of x when y = 0. y
(0, 5)
5 x + 3(0) = 15
5 x = 15
x
x=3 (3, 0)
The y-intercept is the value of y when x = 0.
5(0) + 3 y = 15
3 y = 15
y =5

24. homework
Evaluate each function rule for x = –5.
1. y = x – 7 2. y = 7 – x
3. y = 2x + 5 4. y = – x + 3
Draw the graph of y= 5x + 4
Find x and y intercepts of f(X)

25. references
Bibliography
Fant, R. (2005). linear equations., (pp.
15-17).
Glencoe. (2005). algebra2.
Ridgell. (n.d.). rate of change and slope.,
(p. chapter 6).