Straight Lines

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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
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The Gradient of a straight line
Complete the table for the equation y x
Straight Lines
x -3 -1 0 1 3
y          
-3
-1
0
3
1
Complete the table for the equation y 2x
x -3 -1 0 1 3
y          
-6
-2
0
6
2
Complete the table for the equation y 3x
x -3 -1 0 1 3
y          
-9
-3
0
9
3
Complete the table for the equation y -x
x -3 -1 0 1 3
y          
3
1
0
-3
-1
3
Straight Lines
What do you notice about these straight lines?
They are not parallel - they have different
gradients
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Straight Lines
We look at the gradient more closely
5 4 3 2 1
           
           
           
           
           
y x
if x 1 then y 1
if x 2 then y 2
So we say
x
every time we go across 1 we go up 1
x
0 1 2 3 4 5 6
5
Straight Lines
           
5 4 3 2 1
           
           
           
           
           
y 2x
x
if x 0 then y 0
if x 1 then y 2
if x 2 then y 4
x
So we say
every time we go across 1 we go up 2
x
0 1 2 3 4 5 6
6
Straight Lines
x
           
5 4 3 2 1
           
           
           
           
           
y 3x
if x 0 then y 0
x
if x 1 then y 3
if x 2 then y 6
So we say
every time we go across 1 we go up 3
x
0 1 2 3 4 5 6
7
Straight Lines
y -x
2 1 0 -1 -2
           
           
           
           
           
if x 0 then y 0
if x 1 then y -1
if x 2 then y -2
x
0 1 2 3 4 5 6
So we say
x
every time we go across 1 we go down 1
x
negative gradient A negative coefficient for x
positive gradient A positive coefficient for x
e.g. y -x, y -2x, y -3x
e.g. y x, y 2x, y 3x
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Straight Lines
To summarise for the gradient of a line
The coefficient of x tells us the gradient of a
straight line (how steep it is)
A gradient of 1 every time we go across 1 we go
up 1
y x
y 2x
A gradient of 2 every time we go across 1 we go
up 2
Steeper than a gradient of 1
y 3x
A gradient of 3 every time we go across 1 we go
up 3
Steeper than a gradient of 2
y -x
A gradient of -1 every time we go across 1 we go
down 1
A negative gradient
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Straight Lines
To summarise for any straight line
For any equation in the form y mx c
The variable m can be or -
m is the gradient
c is the y-intercept
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Straight Lines
Finding the gradient for the line that passes
through two pairs of coordinates
The gradient is the same at every point on the
straight line.
To find the gradient between two points find how
much it has gone up and compare this with how
much it has gone across.
x
How much up (y-direction)
difference in y
x
How much across (x-direction)
difference in x
gradient
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Straight Lines
Find the gradient for the line that passes
through (2,1) and (5,7)
difference in y
7 1 6
difference in x
5 2 3
x
6 3
gradient
2
In general terms we can say (2,1) is
(x1,y1) and (5,7) is (x2,y2)
x
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Straight Lines
Now do these
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Worksheet 1
Complete the table for the equation y x
Straight Lines
x -3 -1 0 1 3
y          
Complete the table for the equation y 2x
x -3 -1 0 1 3
y          
Complete the table for the equation y 3x
x -3 -1 0 1 3
y          
Complete the table for the equation y -x
x -3 -1 0 1 3
y