Straight Lines
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
Straight Lines
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
y = x + 10
for x = 2
for x = 3
y=4
y = 13
y=x+3
y=x–2
for x = -6
for x = 3
y = -3
y=1
-3
y = -6
y = x -3
y = 2x - 5
y = -3x -5
y = -6x + 5
for x =
for x = 5
y=5
for x = 2.5
for x = -3.5
y = -12.5
y = 26
Straight Lines
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:
y=x+2
x -3 -2 -1 0
1
2
3
y -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)
Plotting these points
(-3,-1)
(-2,0)
(-1, 1)
(0, 2)
Straight Lines
(0, 2)
(1, 3)
(2, 4)
(3, 5)
y
10
9
8
7
6
5
4
3
x
x
x
x
x
2
We find a straight line-10
x1
-9
-8
-7
-6 -5
-4
-3
x
x -1
-2
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9
10
x
Straight Lines
Copy and complete this table for the following equation and plot the
y
straight line
10
9
y = 3x - 1
x
8
7
6
x
y
-3 -1
-10 4
0
-1
1
2
3
8
5
4
3
2
x
1
-10 -9
-8
-7
-6 -5
-4
-3
-2
-1
0
x
-1
-2
-3
x -4
-5
-6
-7
-8
x
-9
-10
1
2
3
4
5
6
7
8
9
10
x
Complete the table for
the equation y = x
x -3 -1 0 1
1
y -3 -1 0
Complete the table for
the equation y = x +1
x -3 -1 0 1
-2
0
1 2
y
Complete the table for
the equation y = x + 3
x -3 -1 0 1
2
3 4
0
y
Complete the table for
the equation y = x - 2
x -3 -1 0 1
y -5 -3 -2 -1
Straight Lines
3
3
Plot the coordinates
When the table is completed
y
10
9
8
7
3
4
5
4
x
3
-10 -9
3
6
-8
-7
-6 -5
-4
x
x
x
x2 x
x
1x x
x xx1 2 3 4
-3 -2 -1 0
x -1 x
x
-2x
x x -3
x
-4
-5
-6
3
1
x
6
-7
-8
-9
-10
5
6
7
8
9
10
x
Straight Lines
What do you notice about these straight lines?
y=x
y=x+1
y=x+3
y=x-2
y
10
9
8
7
5
4
They are parallel to each
other
i.e. they have the same -10
gradient
The number added to x
is where the line crosses
the y axis
x
6
x
3
-9
-8
-7
-6 -5
-4
x
x
x
x2 x
x
1x x
x xx1 2 3 4
-3 -2 -1 0
x -1 x
x
-2x
x x -3
x
-4
-5
-6
-7
-8
-9
-10
5
6
7
8
9
10
x
Straight Lines
We start with the line y = x
y
10
To become y = x + 1
The line moves up by 1
and crosses the y axis at 1
9
8
7
6
5
4
Start again with the line y = x
To become y = x + 4
3
2
1
The line moves up by 4
and crosses the y axis at 4
-10 -9
-8
-7
-6 -5
-4
-3
-2
-1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9
10
x
Straight Lines
Write the equations of these lines?
1
2
3
4
5
1
y
10
y=x+6
y=x+2
y=x-1
y=x-5
y=x-9
2
9
8
7
3
6
5
4
4
3
2
5
1
-10 -9
-8
-7
-6 -5
-4
-3
-2
-1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9
10
x
Straight Lines
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
Straight Lines
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
1
2
3
4
5
6
7
8
9
10
x
Complete the table for
the equation y = x
x -3 -1 0 1
y
Complete the table for
the equation y = x +1
x -3 -1 0 1
y
Complete the table for
the equation y = x + 3
x -3 -1 0 1
y
Complete the table for
the equation y = x - 2
x -3 -1 0 1
y
Worksheet 1
Straight Lines
Plot the coordinates
When the table is completed
y
3
10
9
8
7
6
3
5
4
3
2
1
-10 -9
3
-8
-7
-6 -5
-4
-3
-2
-1
0
-1
-2
-3
-4
-5
-6
3
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9
10
x
Worksheet 2
Straight Lines
Write the equations of these lines?
1
y
10
1
2
3
4
5
2
9
8
7
3
6
5
4
4
3
2
5
1
-10 -9
-8
-7
-6 -5
-4
-3
-2
-1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9
10
x