y = mx + cStarter Activity: Guess the Rule

0123-4y = 2x + 2

24686

x y0123-4y = 2x + 1

-2147

-14

x y

y = mx + cStarter Activity: Guess the Rule

3456-4

y = 10x + 3

33435363-37

x y2468-4y = 4x + 2

10182634-14

x y

y = mx + cStarter Activity: Guess the Rule

20212223-4y = 5x - 4

9610110611124

x y0123-4

y = -2x + 2

20-2-410

x y

OBJECTIVE:By the end of the lesson you should…

…be able to …

• … find the equation for any linear graph from the diagram

(All pupils)

• … find the equation of any line given any two points on the line

(Most pupils)

• … use these skills to interpret real life problems

(Some pupils)

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 Line Graphs (y = mx + c)

m gives the gradient of the line and c gives the y intercept.

All straight line graphs are of the form y = mx + c

The gradient is defined as the Change in yChange in x

ch y = 2ch x =

1

y intercept = 3

y = 2x + 3

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 Line Graphs (y = mx + c)

m gives the gradient of the line and c gives the y intercept.

All straight line graphs are of the form y = mx + c

The gradient is defined as the Change in yChange in x

ch y = 3

ch x = 1

y intercept = -4

y = 3x - 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

Straight Line Graphs (y = mx + c)

m gives the gradient of the line and c gives the y intercept.

All straight line graphs are of the form y = mx + c

The gradient is defined as the Change in yChange in x

ch y = 1ch x =

2

y intercept = 1

y = ½x + 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

Straight Line Graphs (y = mx + c)

m gives the gradient of the line and c gives the y intercept.

All straight line graphs are of the form y = mx + c

The gradient is defined as the Change in yChange in x

ch y = 1ch x =

3

y intercept = -5

1y= x- 5

3

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 Line Graphs (y = mx + c)

m gives the gradient of the line and c gives the y intercept.

All straight line graphs are of the form y = mx + c

The gradient is defined as theChange in yChange in x

ch y = 3

ch x = 4

y intercept = 2

3y= x +2

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

Straight Line Graphs (y = mx + c)

m gives the gradient of the line and c gives the y intercept.

All straight line graphs are of the form y = mx + c

The gradient is defined as the Change in yChange in x

ch y = 4

ch x = 5

y intercept = 3

4y=- x +3

5

Key Questions:Find the formulae for these Real Life Problems

(1) A taxi firm has a formula for working out fares

It is in the form P=mN + c P=Price

N = No. miles

A 0 mile journey costs £2A 2 miles journey costs £6(2) A taxi firm has a formula for working out fares

It is in the form P=mN + c P=Price

N = No. cards

60 cards cost £155110 cards cost £255Hint: If it helps then quickly sketch the graphs with N going

across and P going up

OBJECTIVE:Have you met your lesson objectives?

Are you able to …

• … find the equation for any linear graph from the diagram

(All pupils)

• … find the equation of any line given any two points on the line

(Most pupils)

• … use these skills to interpret real life problems

(Some pupils)