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1. October 4, 2012
Linear graphs I
1. The four quadrants
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2. Explanation y
October 4, 2012
4 October
This is called the Cartesian plane. 8
7
It is named after the French 6
mathematician, philosopher and 5
y
4
scientist René Descartes. 3
A
D2
The scales can extend as far
1
as you want in each direction.
-23 -22 -21 -20 -19 -18 17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 x5 x
The plane consists of four C
-1
-2
quadrants. -3
B
You can plot points in any of the -4
-5
four quadrants, using positive -6 A ( 2,3)
and negative coordinates. -7
B (3,-3)
-8
The first number is along the x axis, -9 C (-2,-2)
the second number is up or down the y axis. D (-1,2) -10
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3. Explanation October 4, 2012
Look at this line.
At any point on this line, the y coordinate is 3.
This line has the equation y = 3. y
4
What would the line for the 3
equation x = 1 look like? 2
1
The x axis has the equation y = 0. -4 -3 -2 -1 0 1 2 3 4 x
-1
-2
The y axis has the equation x = 0. -3
-4
y = 3 is the equation of the line that passes through 3 on
the y axis and is parallel to y = 0.
x = 1 is the equation of the line that passes through 1 on
the x axis and is parallel to x = 0.
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4. Explanation October 4, 2012
Very often you need to draw a graph y
that takes the form: 10
9
y = a multiple of x plus another number 8
y = 2x + 3
or y = mx + c 7
6
This means that every y coordinate 5
4
can be calculated by multiplying 3
each x coordinate, then adding 2
another number. 1
Always calculate three values for y. -3 -2 -1 0
-1
1 2 3x
If y = 2x + 3 -2
-3
When x = 2 y = 2 × 2 + 3 = 7 ( 2,7 ) -4
When x = -3 y = 2 × -3 + 3 = -3 (-3,-3)
When x = 0 y = 2 × 0 + 3 = 3 ( 0,3 )
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5. Example October 4, 2012
Draw the graph for y = -2x + 2 y
10
Make sure that you calculate and y = -2x + 2 9
write down your three coordinates. 8
7
When x = -1 y = -2 × -1 + 2 = 4 ( -1,4 ) 6
5
When x = 3 y = -2 × 3 + 2 = -4 ( 3,-4 ) 4
3
When x = 0 y = -2 × 0 + 2 = 2 ( 0,2 ) 2
1
Plot your three points. -3 -2 -1 0 1 2 3x
Carefully join all three points with a -1
-2
straight line, using a ruler. -3
Always label your line. -4
For all equations of the type y = mx + c, the line will
cross the y axis at the point y = c.
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