Download presentation

Presentation is loading. Please wait.

1
Straight Line Graphs

2
**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 4) Plotting a Straight Line – X = 0, Y = 0 Method 5) Supporting Exercises Co-ordinates Negative Numbers Substitution

3
**Naming horizontal and vertical lines**

y 1 -5 -4 -3 -2 -1 4 3 2 5 (x,y) (3,4) (3,1) x y = -2 (-4,-2) (0,-2) (-4,-2) (3,-5) x = 3 Back to Main Page

4
**Now try these lines y (x,y) (-2,4) y = 2 (-2,1) x (-4,2) (0,2) (-4,2)**

-5 -4 -3 -2 -1 4 3 2 5 (x,y) (-2,4) y = 2 (-2,1) x (-4,2) (0,2) (-4,2) (-2,-5) x = -2 Back to Main Page

5
**See if you can name lines 1 to 5**

(x,y) y x = 1 x = 5 4 x = -4 3 2 y = 1 1 1 x -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 y = -4 4 -4 -5 5 2 3 Back to Main Page

6
**Diagonal Lines (x,y) y y = x (-3,3) (3,3) (-1,1) (1,1) x (2,-2)**

-5 -4 -3 -2 -1 4 3 2 5 y = x (-3,3) (3,3) (-1,1) (1,1) x (2,-2) (-3,-3) (-4,-3) (0,1) (2,3) y = -x Back to Main Page

7
**Now see if you can identify these diagonal lines**

y = x + 1 1 -5 -4 -3 -2 -1 4 3 2 5 3 y = x - 1 y = - x - 2 x y = -x + 2 4 1 2 Back to Main Page

8
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 Back to Main Page

9
**y x Finding m and c Find the Value of c**

1 2 3 4 5 6 7 8 –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. So c = 3 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. y = 2x +3 y = mx +c So m = 2 Back to Main Page

10
**y x Finding m and c Find the Value of c**

1 2 3 4 5 6 7 8 –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. y = mx +c y = 2x +3 So c = 2 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 Back to Main Page

11
**y x Some Lines to Identify 1 2 y = x + 2 1 -1 y = x - 1 -2 1**

1 2 3 4 5 6 7 8 –7 –6 –5 –4 –3 –2 –1 -1 -2 -3 -4 -5 -6 Line 1 m = c = Equation: 1 2 y = x + 2 Line 2 m = c = Equation: 1 -1 y = x - 1 Line 3 m = c = Equation: -2 1 y = -2x + 1 Back to Main Page

12
**y x Exercise 5 Click for Answers 1) y = x - 2 3 2) y = -x + 3**

1 2 3 4 5 6 7 8 –7 –6 –5 –4 –3 –2 –1 -1 -2 -3 -4 -5 -6 5 Click for Answers 3 1) y = x - 2 2) y = -x + 3 3) y = 2x + 2 4) y = -2x - 1 y = -2x - 1 2 2 1 4 Back to Main Page

13
**Further Exercise Sketch the following graphs by using y=mx + c**

1) y = x + 4 2) y = x - 2 3) y = 2x + 1 4) y = 2x – 3 5) y = 3x – 2 6) y = 1 – x 7) y = 3 – 2x 8) y = 3x 9) y = x + 2 2 10) y = - x + 1 Back to Main Page

14
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 = y = 2(0) y = 1 x 1 2 y 3 5 x = y = 2(1) y = 3 x = y = 2(2) y = 5 Now you just have to plot the points on to a graph! Back to Main Page

15
**The Table Method x 1 2 y 1 3 5 4 3 2 1 -4 -3 -2 -1 1 2 3 4 -1 -2**

1 2 y 4 3 1 3 5 2 1 -4 -3 -2 -1 1 2 3 4 -1 -2 y = 2x + 1 -3 -4 Back to Main Page

16
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 1 2 y Click to reveal plotted lines Back to Main Page

17
**The Table Method 4 3 2 1 -4 -3 -2 -1 1 2 3 4 -1 -2 -3 3 1 -4 4 2**

1 2 3 4 -1 -2 -3 3 1 Click for further exercises -4 4 2 Back to Main Page

18
**Further Exercise Using the table method, plot the following graphs.**

1) y = x + 2 2) y = x – 3 3) y = 2x + 4 4) y = 2x – 3 5) y = 3x + 1 6) y = 3x – 2 7) y = 1 – x 8) y = 1 – 2x 9) y = 2 – 3x 10) y = x + 1 2 2 Back to Main Page

19
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. Back to Main Page

20
**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). Back to Main Page

21
**y x 8 7 6 5 This is where the graph cuts the x – axis (y=0) 4 3**

1 2 3 4 5 6 7 8 -1 -2 -3 -4 -5 -6 This is where the graph cuts the x – axis (y=0) This is where the graph cuts the y – axis (x=0) Back to Main Page

22
**By substituting these values into the equation we can find the other half of the co-ordinates.**

Back to Main Page

23
**Example Question: Draw the graph of 2x + y = 4 Solution x = 0**

1st Co-ordinate = (0,4) y = 0 2x + 0 = 4 2x = 4 x = 2 2nd Co-ordinate = (2,0) Back to Main Page

24
**y x So the graph will look like this. 2x + y = 4 1 2 3 4 5 6 7 8 1 2 3**

1 2 3 4 5 6 7 8 –7 –6 –5 –4 –3 –2 –1 -1 -2 -3 -4 -5 -6 2x + y = 4 Back to Main Page

25
**Exercise Plot the following graphs using the x=0, y=0 method.**

Click to reveal plotted lines Back to Main Page

26
**y x Answers 3x + 2y = 6 x + 2y = 2 2x + 3y = 6 x - 3y = 3**

1 2 3 4 5 6 7 8 –7 –6 –5 –4 –3 –2 –1 -1 -2 -3 -4 -5 -6 Answers 3x + 2y = 6 x + 2y = 2 2x + 3y = 6 x - 3y = 3 Click for further exercises Back to Main Page

27
**Exercise Using the x = 0, y = 0 method plot the following graphs:**

Back to Main Page

28
**What are the Co-ordinates of these points?**

-1 1 -5 -4 -3 -2 5 4 3 2 (x,y) Mention the order of cartesian co-ordiantes (x is a-cross) Back to Main Page

29
**Negative Numbers (1) 2 + 3 (2) 6 - 5 (3) 3 - 7 (4) -2 + 6**

Addition and Subtraction (1) (2) (3) (4) (5) (6) (7) (8) 0 – 4 (9) (10) (11) (12) (13) (14) (- 2) (15) (- 1) (16) (17) (18) 14 - (- 2) (19) (20) 4 - 5½ Back to Main Page

30
**Negative Numbers (1) 4 x -3 (2) -7 x -2 (3) -5 x 4 (4) 28 ÷ -7**

Multiplication and Division (1) x -3 (2) -7 x -2 (3) x 4 (4) 28 ÷ -7 (5) ÷ -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 Back to Main Page

31
**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 2 8 14 -3 -5 6) x 7) x - 3 2 8) x 9) 2x – 6 -4 -1 1 2 Click forward to reveal answers Back to Main Page

32
**Substituting Negative Numbers into Formulae**

Exercise Substitute x = -1 into the following formulae: 1) x – 2 2) 2x 3) 3x + 2 4) 1 – x 5) 3 – 2x -3 -2 -1 2 5 6) x 7) x - 3 2 8) x 9) 2x – 6 6 -3½ 3½ -8 Click forward to reveal answers Back to Main Page

Similar presentations

OK

DIVIDING INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.

DIVIDING INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on fibonacci numbers sequence Free download ppt on relationship between science technology and engineering Ppt on different types of computer softwares stores Ppt on renewable energy resources in india Ppt on food security in india Convert free pdf to ppt online converter Ppt on federalism in india Ppt on area of parallelogram video Ppt on statistics and probability help Ppt on tourism and hospitality