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Straight LinesStraight Lines
Objectives:E Grade Plot the graphs of straight lines such as
x = 3 and y = 4 Complete a table of values for equationssuch as y = 3x + 1 and draw the graph
D Grade Solve problems involving graphs, such as findingwhere the line y = x +3 crosses the line y = 2
C Grade Recognise the equations of straight line graphssuch as y = -3x + 1Find the gradients of straight line graphs
Prior knowledge: Plot co-ordinates in all four quadrants
Straight LinesStraight Lines
In order to plot straight lines we must be able to substitutenumbers 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 = -6x + 5 for x = -3.5
y = -3x -5 for x = 2.5
y = 2x - 5 for x = 5
y = 4 y = 13
y = -3
y = 1
y = -6
y = 5
y = -12.5
y = 26
x -3 -2 -1 0 1 2 3
y
Straight LinesStraight 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
-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)
Straight LinesStraight Lines(-3,-1)(-2,0)(-1, 1)
(0, 2)
(0, 2)(1, 3)
(2, 4)(3, 5)
0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Plotting these points
xxxxxxxx
We find a straight line
Straight LinesStraight Lines
Copy and complete this table for the following equation and plot thestraight line
y = 3x - 1
0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
x -3 -1 0 1 3y -10 -4 -1 2 8
x
x
x
x
x
Straight LinesStraight Lines
0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Complete the table for the equation y = x
x -3 -1 0 1 3y
x -3 -1 0 1 3y
x -3 -1 0 1 3y
x -3 -1 0 1 3y
Complete the table for the equation y = x - 2
Complete the table for the equation y = x + 3
Complete the table for the equation y = x +1
Plot the coordinatesWhen the table is completed
-3 -1 0 1 3
x
xx
x
x-2 0 1 2 4
x
xx
x
x
0 2 3 4 6
x
xx
x
x
-5 -3 -2 -1 1
x
xx
x
x
Straight LinesStraight Lines
0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
x
xx
x
x
x
xx
x
x
x
xx
x
x
x
xx
x
x
What do you notice about these straight lines?
y = x y = x + 1y = x + 3y = x - 2
They are parallel to eachother i.e. they have the same gradient
The number added to xis where the line crossesthe y axis
Straight LinesStraight Lines
0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
We start with the line y = x
y = x + 1To becomeThe line moves up by 1
Start again with the line y = xy = x + 4To become
The line moves up by 4
and crosses the y axis at 1
and crosses the y axis at 4
Straight LinesStraight Lines
0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Write the equations of these lines?
12345
1
2
3
4
5
y = x + 6y = x + 2y = x - 1y = x - 5y = x - 9
Straight LinesStraight 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 LinesStraight Lines
0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Straight LinesStraight Lines
0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Complete the table for the equation y = x
x -3 -1 0 1 3y
x -3 -1 0 1 3y
x -3 -1 0 1 3y
x -3 -1 0 1 3y
Complete the table for the equation y = x - 2
Complete the table for the equation y = x + 3
Complete the table for the equation y = x +1
Plot the coordinatesWhen the table is completed
Worksheet 1
Straight LinesStraight Lines
0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x
y
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
Write the equations of these lines?
12345
1
2
3
4
5
Worksheet 2