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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)