straight line graphs
DESCRIPTION
Straight Line Graphs. Straight Line Graphs. Sections 1) 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) - PowerPoint PPT PresentationTRANSCRIPT
Straight Line Graphs
Straight Line GraphsSections
1) 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
x
y
1
-5
-4
-3
-2
-1
4
3
2
1
-5 -4 -3 -2 0 2 3 54-1
Naming horizontal and vertical lines
(-4,-2) (0,-2) (-4,-2)
y = -2
(3,4)
(3,1)
(3,-5)x = 3
(x,y)
Back to Main Page
1
-5
-4
-3
-2
-1
4
3
2
1
-5 -4 -3 -2 0 2 3 54-1
Now try these lines
(-4,2) (0,2) (-4,2)
y = 2
(-2,4)
(-2,1)
(-2,-5)x = -2
(x,y)
Back to Main Page
y
x
-5
-4
-3
-2
-1
4
3
2
1
1-5 -4 -3 -2 0 2 3 54-1
See if you can name lines 1 to 5(x,y)
1
5 3
4
2 Back to Main Page
y
x
y = 1
x = 1 x = 5
y = -4
x = -4
1
-5
-4
-3
-2
-1
4
3
2
1
-5 -4 -3 -2 0 2 3 54-1
Diagonal Lines
(-4,-3) (0,1) (2,3)
(3,3)
(1,1)
(-3,-3)
y = -x
(x,y)
Back to Main Page
(2,-2)
(-1,1)
(-3,3)
y = x
y = x + 1y
x
Back to Main Page
1 2
1
-5
-4
-3
-2
-1
4
3
2
1
-5 -4 -3 -2 0 2 3 54-1
3
4
Now see if you can identify these diagonal lines
x
y
y = x - 1
y = x + 1
y = - x - 2
y = -x + 2
y = mx + cEvery straight line can be written in this form. To do this the values for m and c must be found.
y = mx + cc is known as the intercept
m is known as the gradient
Back to Main Page
y
x 1 2 3 4 5 6 7 8
12345678
–7 –6 –5 –4 –3 –2 –1 -1-2-3-4-5-6
Find the Value of c
This is the point at which the line crosses the y-axis.
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.
Finding m and c
y = 2x +3y = mx +c
So c = 3
So m = 2
Back to Main Page
y
x 1 2 3 4 5 6 7 8
12345678
–7 –6 –5 –4 –3 –2 –1 -1-2-3-4-5-6
Find the Value of c
This is the point at which the line crosses the y-axis.
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.
Finding m and c
y = 2x +3y = mx +cSo c = 2
So m = -1
Back to Main Page
y
x 1 2 3 4 5 6 7 8
12345678
–7 –6 –5 –4 –3 –2 –1 -1-2-3-4-5-6
Line 1
m =
c =
Equation:
Some Lines to Identify
Line 2
m =
c =
Equation:
12
y = x + 2
Line 3
m =
c =
Equation:
1-1
y = x - 1
-21
y = -2x + 1Back to Main Page
y
x 1 2 3 4 5 6 7 8
12345678
–7 –6 –5 –4 –3 –2 –1 -1-2-3-4-5-6
Exercise
Back to Main Page
Click for Answers
12
3
5
4
1) y = x - 2
2) y = -x + 3
3) y = 2x + 2
4) y = -2x - 1
5) y = -2x - 1
2
Further ExerciseSketch the following graphs by using y=mx + c
1) y = x + 42) y = x - 23) y = 2x + 14) y = 2x – 35) y = 3x – 2
6) y = 1 – x7) y = 3 – 2x8) y = 3x9) y = x + 2 210) y = - x + 1 2
Back to Main Page
The Table MethodWe can use an equation of a line to plot a graph by substituting values of x into it.
Example
y = 2x + 1x = 0 y = 2(0) +1 y = 1x = 1 y = 2(1) +1 y = 3
x = 2 y = 2(2) +1 y = 5
Now you just have to plot the points on to a graph!
Back to Main Page
x 0 1 2
y 1 3 5
The Table Method
0 1-1 432-2-3-4-1
-2-3
-4
1
23
4
y = 2x + 1
Back to Main Page
x 0 1 2
y 1 3 5
The Table MethodUse the table method to plot the following lines:
1) y = x + 3
2) y = 2x – 3
3) y = 2 – x
4) y = 3 – 2x
Click to reveal plotted lines
Back to Main Page
x 0 1 2
y
The Table Method
0 1-1 432-2-3-4-1
-2-3
-4
1
23
4
4
31
2 Back to Main Page
Click for furtherexercises
Further ExerciseUsing the table method, plot the following graphs.
1) y = x + 22) y = x – 33) y = 2x + 44) y = 2x – 35) y = 3x + 16) y = 3x – 2
7) y = 1 – x8) y = 1 – 2x
9) y = 2 – 3x10) y = x + 1
2
Back to Main Page
2
This method is used when x and y are on the same side. Example: x + 2y = 4
The x = 0, y = 0 Method
To draw a straight line we only need 2 points to join together.
Back to Main Page
These points are where x = 0 (anywhere along the y axis) and y = 0 (anywhere along the x axis).
If we find the 2 points where the graph cuts the axes then we can plot the line.
Back to Main Page
y
x 1 2 3 4 5 6 7 8
12345678
-6 -5 -4 -3 -2 -1 -1-2-3-4-5-6
This is where the graph cuts the y – axis (x=0)
This is where the graph cuts the x – axis (y=0)
Back to Main Page
By substituting these values into the equation we can find the other half of the co-ordinates.
Back to Main Page
ExampleQuestion: Draw the graph of 2x + y = 4
Solutionx = 02(0) + y = 4
y = 4
1st Co-ordinate = (0,4)
y = 0
2x + 0 = 4
2x = 4
x = 2
2nd Co-ordinate = (2,0)
Back to Main Page
So the graph will look like this.y
x 1 2 3 4 5 6 7 8
12345678
–7 –6 –5 –4 –3 –2 –1 -1-2-3-4-5-6
2x + y = 4
Back to Main Page
ExercisePlot 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
Back to Main Page
Answersy
x 1 2 3 4 5 6 7 8
12345678
–7 –6 –5 –4 –3 –2 –1 -1-2-3-4-5-6
1. 3x + 2y = 62. x + 2y = 23. 2x + 3y = 64. x - 3y = 3
Click for furtherexercises
Back to Main Page
Exercise
1) x + y = 4
2) 2x + y = 2
3) x + 2y = 2
4) x + 3y = 6
5) 2x + 5y = 10
6) x – y = 3
7) 2x – y = 2
8) 2x – 3y = 6
9) x + 2y = 1
10) 2x – y = 3
Back to Main Page
Using the x = 0, y = 0 method plot the following graphs:
What are the Co-ordinates of these points?
-11
-5
-4
-3
-2
5
4
3
2
1
-5 -4 -3 -2 0 2 3 54-1
(x,y)
Back to Main Page
Negative Numbers
(1) 2 + 3 (2) 6 - 5 (3) 3 - 7 (4) -2 + 6
(5) -1 - 2 (6) -4 + 5 (7) -2 - 2 (8) 0 – 4
(9) -3 + 6 (10) -4 - 1 (11) 6 - 8 (12) -5 - 2
(13) -8 + 4 (14) -5 - (- 2) (15) 0 - (- 1)
(16) 7 - 12 + 9 (17) -4 - 9 + -2 (18) 14 - (- 2)
(19) -45 + 17 (20) 4 - 5½
Addition and Subtraction
Back to Main Page
Negative Numbers
(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
Multiplication and Division
Back to Main Page
Substituting Numbers into Formulae
Exercise
Substitute x = 4 into the following formulae:
1) x – 2
2) 2x
3) 3x + 2
4) 1 – x
5) 3 – 2x
6) 4 - 2x
7) x - 3 2
8) 3 - x 29) 2x – 6
Click forward to reveal answers
2814-3-5
-4-1
12
Back to Main Page
Substituting Negative Numbers into FormulaeExercise
Substitute x = -1 into the following formulae:
1) x – 22) 2x3) 3x + 24) 1 – x5) 3 – 2x
6) 4 - 2x7) x - 3
2
8) 3 - x 2
9) 2x – 6
Click forward to reveal answers
-3-2-1 2 5
6-3½
3½-8
Back to Main Page