1. 1
Sep 23­03:21 p.m.
Linear functions
During this lesson we will :
• Explore the equation of a straight line.
• Discover algebraic relations between pairs of
parallel and perpendicular lines.
• Explore the absolute value function and its
properties.
• Recognise and draw piecewise linear functions.

2. 2
Sep 23­03:21 p.m.
Distance between two points
A
B

3. 3
Sep 23­03:21 p.m.
The Midpoint formula:
A
B
M
x1 x2

4. 4
Sep 23­03:21 p.m.
Linear functions
The graph is a straight line.

5. 5
Sep 23­03:21 p.m.
Gradient of a line
The gradient of a line is a measure of its steepness
If
and
positive gradient negative gradient

6. 6
Sep 23­03:21 p.m.
horizontal lines have a gradient of 0 (zero)
vertical lines have an undefined gradient
parallel lines have equal gradients
the gradients of perpendicular lines are
negative reciprocals
if the gradients are m1 and m2 then:
or

7. 7
Sep 23­03:21 p.m.
Equations of lines
The equation of a line is an equation which states the connection
betwen the x and y values for every point on the line.
All vertical lines have equations of the form x = a , ( a is a constant)
All horizontal lines have equations of the form y = c , ( c is a constant)
slope-intercept form or explicit form
gradient
y-intercept
general form or implicit form
(not a function)

8. 8
Sep 23­03:21 p.m.
Write down the gradient and y-intercept of these straight
lines:
y = 5x ­ 2
2y = 1 ­ 6 x
3x + 2y ­ 8 = 0

9. 9
Sep 23­03:21 p.m.
Sketch the graphs of these equations:
y = 2 x ­ 1 3y + 2x ­3 = 0 2y ­ x + 1 = 0

10. 10
Sep 23­03:21 p.m.
Write down the equation of the straight line which passes
through the points A (2,5) and B (6,17).

11. 11
Sep 23­03:21 p.m.
Find the explicit and implicit equations of the line
through (-1,3) with a slope of 5.

12. 12
Sep 23­03:21 p.m.
Are L1 with equation 2x ­ y + 2=0 and L2 with equation
x + 4y ­ 1 = 0 perpendicular lines?

13. 13
Sep 23­03:21 p.m.
Find the equation of the line through (1,-5) and (5,-2).
Express the equation in the form Ax+By + C = 0, with A, B and C
integer numbers.

14. 14
Sep 23­03:21 p.m.
Intercepts
x­intercept
y­intercept
x
y
The x-intercept is found by letting y =0.
The y-intercept is found by letting x=0.

15. 15
Sep 23­03:21 p.m.
For the line with equation 2x - 3y =12, find axis intercepts.

16. 16
Sep 23­03:21 p.m.
Find the point of intersection of the lines :
3x+4y=29 and 2x ­ 5y=4
3x+4y=29
2x ­ 5y=4

17. 17
Sep 23­03:21 p.m.
At the end of the lesson:
Reproduce exactly this drawing on your GDC.

18. 18
Sep 23­03:21 p.m.
At the end of the lesson:
Reproduce exactly this drawing on your GDC.

19. 19
Sep 23­03:21 p.m.
Can you give a formula for the following
graph?

20. 20
Sep 23­03:21 p.m.
Piecewise linear functions
Draw the graph of:

21. 21
Sep 23­03:21 p.m.
Absolute value
Examples:
1 ­ |­6| =
|π­3|= |2π­ 7|=

22. 22
Sep 23­03:21 p.m.
Equations:

23. 23
Sep 23­03:21 p.m.
|x|≤3
|x ­ 1 | ≤ 4
In general: | x | ≤ a ⇒ ­a ≤ x ≤ a
­a a0

24. 24
Sep 23­03:21 p.m.
|x|>5
|x ­ 2 | ≥ 4
In general: | x | >a ⇒ x < ­a or x> a
­a a0

25. 25
Sep 23­03:21 p.m.
Absolute value function (Modulus)
Sketch the graph of f(x).

26. 26
Sep 23­03:21 p.m.

27. 27
Sep 23­03:21 p.m.
With calculator: Menu graph
OPTN
Num (F5)
Abs (X)
Casio
TI-84 Y=
MATH > 1 (X )

28. Attachments
Y11 Linear functions 2010.odt