Straight LinesStraight Lines

Objectives:E Grade Plot the graphs of straight lines such as

x = 3 and y = 4 Complete a table of values for equationssuch as y = 3x + 1 and draw the graph

D Grade Solve problems involving graphs, such as findingwhere the line y = x +3 crosses the line y = 2

C Grade Recognise the equations of straight line graphssuch as y = -3x + 1Find the gradients of straight line graphs

Prior knowledge: Plot co-ordinates in all four quadrants

Straight LinesStraight Lines

In order to plot straight lines we must be able to substitutenumbers into an equation in order to calculate a value.

Try these:Using the value given for x, calculate the value for y

y = x + 2 for x = 2y = x + 10 for x = 3y = x + 3 for x = -6y = x – 2 for x = 3

y = x -3 for x = -3

y = -6x + 5 for x = -3.5y = -3x -5 for x = 2.5y = 2x - 5 for x = 5

y = 4 y = 13 y = -3 y = 1

y = -6

y = 5

y = -12.5 y = 26

x -3 -2 -1 0 1 2 3y              

Straight LinesStraight Lines

When given an equation and told to plot a graph, first find coordinates of points on the line, this is done by completing a table.

By substituting the given values for x calculate the y value for the following equation:

y = x + 2

-1 0 1 2 3 4 5

This generates coordinates to plot on a graph

(-3,-1)(-2,0)(-1, 1)(0, 2)

(0, 2)(1, 3)(2, 4)(3, 5)

Straight LinesStraight Lines(-3,-1)(-2,0)(-1, 1)(0, 2)

(0, 2)(1, 3)(2, 4)(3, 5)

0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x

y

1

2

3

4

5

6

7

8

9

10

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

Plotting these points

xxxxxxxx

We find a straight line

Straight LinesStraight Lines

Copy and complete this table for the following equation and plot thestraight line

y = 3x - 1

0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x

y

1

2

3

4

5

6

7

8

9

10

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

x -3 -1 0 1 3y          -10 -4 -1 2 8

x

x

x

x

x

Straight LinesStraight Lines

0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x

y

1

2

3

4

5

6

7

8

9

10

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

Complete the table for the equation y = xx -3 -1 0 1 3y          

x -3 -1 0 1 3y          

x -3 -1 0 1 3y          

x -3 -1 0 1 3y          

Complete the table for the equation y = x - 2

Complete the table for the equation y = x + 3

Complete the table for the equation y = x +1

Plot the coordinatesWhen the table is completed

-3 -1 0 1 3

x

xx

x

x-2 0 1 2 4

x

xx

x

x

0 2 3 4 6

x

xx

x

x

-5 -3 -2 -1 1

x

xx

x

x

Straight LinesStraight Lines

0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x

y

1

2

3

4

5

6

7

8

9

10

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

x

xx

x

x

x

xx

x

x

x

xx

x

x

x

xx

x

x

What do you notice about these straight lines?

y = x y = x + 1y = x + 3y = x - 2

They are parallel to eachother i.e. they have the same gradient

The number added to xis where the line crossesthe y axis

Straight LinesStraight Lines

0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x

y

1

2

3

4

5

6

7

8

9

10

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

We start with the line y = x

y = x + 1To becomeThe line moves up by 1

Start again with the line y = xy = x + 4To become

The line moves up by 4

and crosses the y axis at 1

and crosses the y axis at 4

Straight LinesStraight Lines

0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x

y

1

2

3

4

5

6

7

8

9

10

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

Write the equations of these lines?

12345

1

2

3

4

5

y = x + 6y = x + 2y = x - 1y = x - 5y = x - 9

Straight LinesStraight Lines

To summarise for where a line crosses the y-axis

Known as the y intercept

For any equation in the form y = x + cThe variable c can be + or -

c is where the line crosses the y axis

Straight LinesStraight Lines

0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x

y

1

2

3

4

5

6

7

8

9

10

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

Straight LinesStraight Lines

0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x

y

1

2

3

4

5

6

7

8

9

10

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

Complete the table for the equation y = xx -3 -1 0 1 3y          

x -3 -1 0 1 3y          

x -3 -1 0 1 3y          

x -3 -1 0 1 3y          

Complete the table for the equation y = x - 2

Complete the table for the equation y = x + 3

Complete the table for the equation y = x +1

Plot the coordinatesWhen the table is completed

Worksheet 1

Straight LinesStraight Lines

0 1 2 3 4 5 6 7 8 9 10-9 -8 -7 -6 -5 -4 -3 -2 -1-10 x

y

1

2

3

4

5

6

7

8

9

10

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

Write the equations of these lines?

12345

1

2

3

4

5

Worksheet 2