Starter QuestionsStarter Questions

Factorise 5x + 10

Learning IntentionLearning Intention

To explain and draw straight lines of the form y = mx + c.

The Straight Line Equation

The Straight Line Equation

x

y

1

2

3

4

5

By calculating the gradient of each line, write down

the equation of the line

The Straight Line Equation

Line 1 Gradient = vertical height horizontal distance

= 4 1

= 4

Equation of line is y = 4x

Line 2 Gradient = vertical height horizontal distance

= 3 2

Equation of line is y = 3x 2

Line 3 Gradient = vertical height horizontal distance

= 2 2

= 1

Equation of line is y = x

The Straight Line Equation

Line 4 Gradient = vertical height horizontal distance

= 1 2

Equation of line is y = 1x 2

Line 5 Gradient = vertical height horizontal distance

= 1 4

Equation of line is y = 1x 4

The Straight Line Equation

All the lines we have previously looked at all passed through the origin at (0,0)

i.e. y = 2x, y = 3x, y = ½x, y = 5x etc…

Gradient = 2

Gradient = 3 Gradient =

5Gradient =

½

What about straight lines that do not pass through the origin

The Straight Line EquationExample

Draw the line of y = 2x on a suitable coordinate diagram

x

y

0 1 2 3 4

0 2 4 6 8

x

y

On the same diagram, draw the graph of y = 2x + 2

x

y

0 1 2 3 4

=2 =4 =6 =8 =10

What do you notice about the second line?

Same gradient, but slightly higher

upy = 2x

y = 2x + 2

2(0)+22(0)+2 2(0)+2 2(3)+2 2(4)+2

The Straight Line EquationExample

Draw the line of y = x on a suitable coordinate diagram

x

y

0 1 2 3 4

0 1 2 3 4

x

y

On the same diagram, draw the graph of y = x + 4

x

y

0 1 2 3 4

4 5 6 7 8

What do you notice about the second line?

Same gradient, but slightly higher

upy = x

y = x + 4

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

y = x

y = 2x + 3

y = 3x+1

y = x - 3

x

y

0

0

2

2

4

4

x

y

0

3

1

5

2

7

x

y

0

1

1

4

2

7

x

y

0

-3

4

1

8

5

The Straight Line EquationOn your 4 quadrant diagram, Draw the lines of the given

equations.

741 2 3 5 6 8 100

1

2

3

4

5

6

7

8

9

10

9 x

All straight lines have the equation of the form

y = mx + c

GradientWhere linemeets y-axis

y

Straight Line Straight Line EquationEquation

Find the equations of the following lines

y = x y = x+4

lines are parallel if they have the same gradient

y = 4x+2 y = -0.5x+2

Now try Ex 4 Ch6 Page 73Start at Q4

Straight Line Straight Line EquationEquation