Transcript Straight Line Graphs

Straight Line Graphs
Straight Line Graphs
1)
Sections
Horizontal, Vertical and Diagonal Lines
(Exercises)
2)
y = mx + c
(Exercises : Naming a Straight Line
Sketching a Straight Line)
3)
Plotting a Straight Line - Table Method
(Exercises)
4)
Plotting a Straight Line – X = 0, Y = 0 Method
(Exercises)
5)
Supporting Exercises
Co-ordinates
Negative Numbers
Substitution
Naming horizontal and vertical lines
y
(x,y)
(3,4)
4
3
2
(3,1)
1
-5
-4
-3
-2
-1
0
-1
1
2
3
4
5
x
y = -2
-2
-3
(-4,-2)
-4
(0,-2)
-5
(-4,-2)
(3,-5)
x=3
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Now try these lines
y
(x,y)
(-2,4)
4
3
-5
-4
-3
-2
-1
2
y=2
1
(-2,1)
0
-1
1
2
3
4
5
x
-2
-3
(-4,2)
-4
(0,2)
x = -2
-5
(-4,2)
(-2,-5)
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See
(x,y)
if you can name lines 1 to 5
y
x=1
x=5
4
x = -4
3
2
y=1
1
1
-5
-4
-3
-2
-1
0
1
2
3
4
5
x
-1
-2
-3
y = -4
4
-4
5
-5
2
3
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Diagonal Lines
(x,y)
y=x+1
y
y=x
4
(-3,3)
(3,3)
3
2
(-1,1)
-5
(1,1)
1
-4
-3
(2,-2)
-2
-1
0
-1
1
2
3
4
x
5
-2
(-3,-3)
-3
(-4,-3)
-4
(0,1)
-5
(2,3)
y = -x
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Now see if you can identify these diagonal lines
y=x+1
y
4
3
y=x-1
3
y=-x-2
2
1
-5
-4
-3
-2
-1
0
-1
-2
1
2
3
4
x
5
y = -x + 2
-3
-4
1
2
-5
4
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y = mx + c
Every straight line can be written in this form. To do this the
values for m and c must be found.
c is known as the intercept
y = mx + c
m is known as the gradient
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Finding m and c
y
8
Find the Value of c
7
This is the point at
which the line crosses
the y-axis.
6
5
4
So c = 3
3
2
1
–7 –6
–5 –4 –3
–2 –1
-1
1
2
3 4
5
-2
-3
-4
-5
-6
yy == mx
2x +3
+c
6
7 8
x
Find the Value of m
The gradient means
the rate at which the
line is climbing.
Each time the lines
moves 1 place to the
right, it climbs up by 2
places.
So m = 2
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Finding m and c
y
8
Find the Value of c
7
This is the point at
which the line crosses
the y-axis.
So c = 2
6
5
yy == mx
2x +3
+c
4
3
2
1
–7 –6
–5 –4 –3
–2 –1
-1
-2
-3
-4
-5
-6
1
2
3 4
5
6
7 8
x
Find the Value of m
The gradient means
the rate at which the
line is climbing.
Each time the line
moves 1 place to the
right, it moves down
by 1 place. So m = -1
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Some Lines to Identify
y
Line 1
8
m =1
7
6
c= 2
5
Equation: y = x + 2
4
Line 2
3
–7 –6
–5 –4 –3
–2 –1
2
m =1
1
c = -1
-1
-2
1
2
3 4
5
6
7 8
x Equation:y = x - 1
Line 3
-3
m = -2
-4
c= 1
-5
-6
Equation: y = -2x + 1
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Exercise
y
5
Click for Answers
8
3
7
6
5
4
1)
y=x-2
2)
y = -x + 3
3)
y = 2x + 2
4)
y = -2x - 1
3
2
1
–7 –6
–5 –4 –3
–2 –1
-1
1
2
3 4
5
6
7 8
x
5) y = -2x - 1
2
-2
-3
2
-4
1
-5
-6
4
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Further Exercise
Sketch the following graphs by using y=mx + c
1)
y=x+4
6)
y=1–x
2)
y=x-2
3)
y = 2x + 1
7)
8)
y = 3 – 2x
y = 3x
4)
y = 2x – 3
9)
5)
y = 3x – 2
y=x+2
2
y=-x+1
2
10)
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The Table Method
We can use an equation of a line to plot a graph by
substituting values of x into it.
Example
y = 2x + 1
x=0
y = 2(0) +1
y=1
x
0
1
2
x=1
y = 2(1) +1
y=3
y
1
3
5
x=2
y = 2(2) +1
y=5
Now you just have to plot the points on to a graph!
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The Table Method
x
y
0
1
1
3
4
2
3
5
2
1
-4 -3
0
-2 -1
1
2
3
4
-1
y = 2x + 1
-2
-3
-4
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The Table Method
Use the table method to plot the following lines:
1)
y=x+3
2)
y = 2x – 3
3)
y=2–x
4) y = 3 – 2x
x
0
1
2
y
Click to reveal plotted lines
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The Table Method
4
3
2
1
-4 -3
0
-2 -1
1
2
3
4
-1
-2
-3
1
3
-4
2
4
Click for further
exercises
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Further Exercise
Using the table method, plot the following graphs.
1) y = x + 2
7)
y=1–x
2) y = x – 3
8)
y = 1 – 2x
2
3) y = 2x + 4
4) y = 2x – 3
9)
y = 2 – 3x
5) y = 3x + 1
10)
y=x+1
6) y = 3x – 2
2
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The x = 0, y = 0 Method
This method is used when x and y are on the same side.
Example:
x + 2y = 4
To draw a straight line we only need 2 points to join
together.
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If we find the 2 points where the graph cuts the
axes then we can plot the line.
These points are where x = 0 (anywhere along the y
axis) and y = 0 (anywhere along the x axis).
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y
8
7
6
5
This is where the graph
cuts the x – axis (y=0)
4
3
2
This is where the graph
cuts the y – axis (x=0)
1
-6
-5 -4 -3 -2 -1 1
1 2 3 4 5 6 7 8
x
-2
-3
-4
-5
-6
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By substituting these values into the equation we
can find the other half of the co-ordinates.
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Example
Question: Draw the graph of 2x + y = 4
Solution
x=0
y=0
2(0) + y = 4
2x + 0 = 4
y=4
2x = 4
x=2
1st Co-ordinate = (0,4)
2nd Co-ordinate = (2,0)
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So the graph will look like this.
y
8
2x + y = 4
7
6
5
4
3
2
1
–7 –6
–5 –4 –3
–2 –1
-1
1
2
3 4
5
6
7 8
x
-2
-3
-4
-5
-6
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Exercise
Plot the following graphs using the x=0, y=0 method.
1)
x+y=5
2)
x + 2y = 2
3)
2x + 3y = 6
4)
x + 3y = 3
Click to reveal plotted lines
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y
8
Answers
7
6
5
1. 3x + 2y = 6
4
2. x + 2y = 2
2
3. 2x + 3y = 6
1
4. x - 3y = 3
3
–7 –6
–5 –4 –3
–2 –1
-1
1
2
3 4
5
6
7 8
x
-2
-3
-4
Click for further
exercises
-5
-6
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Exercise
Using the x = 0, y = 0 method plot the following graphs:
1)
x+y=4
6)
x–y=3
2)
2x + y = 2
7)
2x – y = 2
3)
x + 2y = 2
8)
2x – 3y = 6
4)
x + 3y = 6
9)
x + 2y = 1
5) 2x + 5y = 10
10) 2x – y = 3
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What are the Co-ordinates of these points?
(x,y)
5
4
3
2
1
-5
-4
-3
-2
-1
0
-1
1
2
3
4
5
-2
-3
-4
-5
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Negative Numbers
Addition and Subtraction
(1) 2 + 3
(2)
6-5
(3)
(5) -1 - 2
(6)
-4 + 5 (7)
(9) -3 + 6
(10) -4 - 1
3-7
(4) -2 + 6
-2 - 2
(8) 0 – 4
(11) 6 - 8
(12) -5 - 2
(13) -8 + 4
(14) -5 - (- 2)
(15) 0 - (- 1)
(16) 7 - 12 + 9
(17) -4 - 9 + -2
(18)
(19) -45 + 17
(20)
14 - (- 2)
4 - 5½
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Negative Numbers
Multiplication and Division
(1)
4 x -3
(2)
-7 x -2
(3)
-5 x 4
(4)
28 ÷ -7
(5) -21 ÷ -3
(6)
-20 ÷ 5
(7) -2 x 3 x 2
(8)
-18 ÷ -3 x 2
(9) -2 x -2 x -2
(10)
2.5 x -10
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Substituting Numbers into Formulae
Exercise
Substitute x = 4 into the following formulae:
1)
x–2
2
6)
4 - 2x
-4
2)
2x
8
7)
-1
3)
3x + 2
14
x-3
2
4)
1–x
-3
8)
5)
3 – 2x
-5
9)
3-x
2
2x – 6
Click forward to reveal answers
1
2
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Substituting Negative Numbers into Formulae
Exercise
Substitute x = -1 into the following formulae:
1)
x–2
-3
6)
4 - 2x
2)
2x
-2
7)
3)
3x + 2
-1
x-3
2
4)
1–x
2
8)
5)
3 – 2x
5
3-x
2
2x – 6
9)
Click forward to reveal answers
6
-3½
3½
-8
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