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GRAPHS OF STRAIGHT LINES. This presentation includes the worksheet: “ Graphs of straight lines (basic) ” available at: www.mathsguru.co.uk. y. x. TO DESCRIBE THE POSITION OF AN OBJECT WE CAN USE A SET OF AXES . Co-ordinates: ( 2 , 7 ). 2 along the x -axis ,

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graphs of straight lines

GRAPHS OF STRAIGHT LINES

This presentation includes the worksheet:

“Graphs of straight lines (basic)”

available at: www.mathsguru.co.uk

slide2

y

x

TO DESCRIBE THE POSITION OF AN OBJECT WE CAN USE A SET OF AXES.

Co-ordinates: (2, 7)

2 along the x-axis,

7 along the y-axis.

x = 2, y = 7

Co-ordinates: (-6, 3)

-6 along the x-axis,

3 along the y-axis.

x = -6, y = 3

slide3

y

x

Every point has an x co-ordinate and a y co-ordinate.

x + y = 8

When plotting a graph,

we are interested in ALL

those points whose co-ordinates

satisfy some rule or other.

For example, consider ALL

those points whose co-ordinates

add up to 8.

ALWAYS label the graph!

x y

0 8

1 7

2 6

3 5

etc.

There are billions of such points!

slide4

y

x

We will plot 4 graphs on a single set of axes.

Example 1.

y = x

y = 3x

x y

x y

0

0 

0

0 

3

3 

6

2 

-4

-4 

-9

-3 

y = 2x

y = ½x

x y

x y

0

0 

0

0 

4

8 

6

3 

2

4 

-8

-4 

slide5

y

x

Example 2.

y = x + 2

y = 2x - 3

x y

x y

2

0 

-3

0 

3

1 

-1

1 

4

2 

1

2 

y = x - 4

y = 3x - 5

x y

x y

-5

0 

-4

0 

-2

1 

-3

1 

1

2 

-2

2 

slide6

Lines parallel to the x axis

y

10

9

8

7

6

5

4

3

2

1

x

0

-10

1

2

3

4

5

6

7

9

10

-9

-8

-6

-4

-3

-2

8

-7

-5

-1

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

Lines parallel to the y axis

Y = 8

Y = 4

Y = 2

Y = 0

Y = -3

Y = -8

x = 5

x = 9

x = - 4

x = - 7

x = 0

slide7

y

x

Plot the following 4 graphs on a single set of axes.

Question 1.

a) y = x

b) y = x + 3

c) y = x + 6

d) y = x 4

slide8

y

x

Plot the following 4 graphs on a single set of axes.

Question 2.

a) y = 2x

b) y = 2x + 3

c) y = 2x 1

d) y = 2x 3

slide9

y

x

Plot the following 3 graphs on a single set of axes.

Question 3.

a) y = 10  x

b) y = 8  x

c) y = 4  x

slide10

y

x

Plot the following 3 graphs on a single set of axes.

Question 4.

a) y = 3x

b) y = 3x 3

c) y = 3x + 4

slide11

y

x

Plot the following 4 graphs on a single set of axes.

Question 5.

a) x + y = 9

b) x + y = 6

c) x + y = 3

d) x + y = 0

slide12

y

x

Plot the following 3 graphs on a single set of axes.

Question 6.

a) y = 10  2x

b) y = 6  2x

c) y = 9  3x

slide13

y

x

Plot the following 3 graphs on a single set of axes.

Question 7.

a) y = 8  x

b) y = 8  2x

c) y = 8  4x