This document discusses plotting and graphing straight lines. It explains how to generate points by substituting values into linear equations and completing tables of values. Examples show linear equations in the form y=mx+c, where c represents the y-intercept. The document demonstrates that lines with the same m value but different c values are parallel, and c determines where the line crosses the y-axis. Completing tables of values and plotting points allows straight lines to be graphed.

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