it's very helpful

1. SSttrraaiigghhtt LLiinneess
Objectives:
E Grade Plot the graphs of straight lines such as
x = 3 and y = 4
Complete a table of values for equations
such as y = 3x + 1 and draw the graph
D Grade Solve problems involving graphs, such as finding
where the line y = x +3 crosses the line y = 2
C Grade Recognise the equations of straight line graphs
such as y = -3x + 1
Find the gradients of straight line graphs
Prior knowledge: Plot co-ordinates in all four quadrants

2. SSttrraaiigghhtt LLiinneess
In order to plot straight lines we must be able to substitute
numbers into an equation in order to calculate a value.
Try these:
Using the value given for x, calculate the value for y
y = x + 2 for x = 2
y = x + 10 for x = 3
y = x + 3 for x = -6
y = x – 2 for x = 3
y = x -3 for x = -3
y = 2x - 5 for x = 5
y = -3x -5 for x = 2.5
y = -6x + 5 for x = -3.5
y = 4
y = 13
y = -3
y = 1
y = -6
y = 5
y = -12.5
y = 26

3. SSttrraaiigghhtt LLiinneess
When given an equation and told to plot a graph, first find
coordinates of points on the line, this is done by completing a table.
By substituting the given values for x calculate the y value for
the following equation:
x -3 -2 -1 0 1 2 3
y
y = x + 2
-1 0 1 2 3 4 5
This generates coordinates to plot on a graph
(-3,-1)
(-2,0)
(-1, 1)
(0, 2)
(0, 2)
(1, 3)
(2, 4)
(3, 5)

4. SSttrraaiigghhtt LLiinneess
(-3,-1)
(-2,0)
(-1, 1)
(0, 2)
(0, 2)
(1, 3)
(2, 4)
(3, 5)
y
10
9
8
7
6
5
4
3
2
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Plotting these points
x
x
x
x
x
x
x
x
We find a straight line

5. SSttrraaiigghhtt LLiinneess
Copy and complete this table for the following equation and plot the
straight line
y = 3x - 1
y
10
9
8
7
6
5
4
3
2
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
x -3 -1 0 1 3
y -1 0 -4 -1 2 8
x
x
x
x
x

6. SSttrraaiigghhtt LLiinneess
y
10
9
8
7
6
5
-2 0 1 2 4
4
x 3
2
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Complete the table for
the equation y = x
x -3 -1 0 1 3
y
Complete the table for
the equation y = x +1
x -3 -1 0 1 3
y
Complete the table for
the equation y = x + 3
x -3 -1 0 1 3
y
Complete the table for
the equation y = x - 2
x -3 -1 0 1 3
y
Plot the coordinates
When the table is completed
-3 -1 0 1 3
x
x
x
x
x
x
x
x
x
0 2 3 4 6
x
x
x
x
x
-5 -3 -2 -1 1
x
x
x
x
x

7. SSttrraaiigghhtt LLiinneess
y
10
9
8
7
6
5
4
3
2
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
What do you notice about these straight lines?
y = x
y = x + 1
y = x + 3
y = x - 2
They are parallel to each
other
i.e. they have the same
gradient
The number added to x
is where the line crosses
the y axis

8. SSttrraaiigghhtt LLiinneess
y
10
9
8
7
6
5
4
3
2
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
We start with the line y = x
To become y = x + 1
The line moves up by 1
and crosses the y axis at 1
Start again with the line y = x
To become y = x + 4
The line moves up by 4
and crosses the y axis at 4

9. SSttrraaiigghhtt LLiinneess
y
10
9
8
7
6
5
4
3
2
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Write the equations of these lines?
1
2
3
4
5
1
2
3
4
5
y = x + 6
y = x + 2
y = x - 1
y = x - 5
y = x - 9

10. SSttrraaiigghhtt LLiinneess
To summarise for where a line crosses the y-axis
Known as the y intercept
For any equation in the form y = x + c
The variable c can be + or -
c is where the line crosses the y axis

11. SSttrraaiigghhtt LLiinneess
y
10
9
8
7
6
5
4
3
2
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10

12. SSttrraaiigghhtt LLiinneess
y
10
9
8
7
6
5
4
3
2
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Complete the table for
the equation y = x
x -3 -1 0 1 3
y
Complete the table for
the equation y = x +1
x -3 -1 0 1 3
y
Complete the table for
the equation y = x + 3
x -3 -1 0 1 3
y
Complete the table for
the equation y = x - 2
x -3 -1 0 1 3
y
Plot the coordinates
When the table is completed
Worksheet 1

13. SSttrraaiigghhtt LLiinneess
y
10
9
8
7
6
5
4
3
2
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 x
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Write the equations of these lines?
1
2
3
4
5
1
2
3
4
5
Worksheet 2