1. Objective
Understand that all straight line graphs can be represented in the form y=mx+c, and be able to state the equation of given graphs

2. Starter: What are the co-ordinates?y x 1 2 3 4 5 6 7 8
–7 –6 –5 –4 –3 –2 –1 -1 -2 -3 -4 -5 -6
(-4, -2)
(4, 6)
(-1, 1)
(6, 5)
(4, -2)
(5, 3)
(2, -3)
(3, 2)
(7, 1)
(-2, -4)
(1, 5)
(-7, 2)
(-4, 3)
(-2, -1)
Skip Starter

3. All straight lines can be written in the form y = mx + c
Knowledge:
All straight lines can be written in the form y = mx + c
You need to be able to write down the equation of a straight line by working out the values for m and c.
It’s not as hard as you might think!

4. c is the constant value – this part of the function does not change.
y = mx + c
m is the gradient of the line
Why use m?
This type of equation was made popular by the French Mathematician Rene Descartes.
“m” could stand for “Monter” – the French word meaning “to climb”.

5. y x Finding m and c Look at the straight line. 1 2 3 4 5 6 7 8
–7 –6 –5 –4 –3 –2 –1 -1 -2 -3 -4 -5 -6
It is very easy to find the value of c – this is the point at which the line crosses the y-axis
So c = 3
Finding m is also easy in this case. The gradient means the rate at which the line is climbing.
Each time the lines moves 1 place to the right, it climbs up by 2 places.
y = mx +c
y = 2x +3
So m = 2

6. y x Another example We can see that c = -2 1 2 3 4 5 6 7 8
–7 –6 –5 –4 –3 –2 –1 -1 -2 -3 -4 -5 -6
As the line travels across 1 position, it is not clear how far up it has moved.
But… Any right angled triangle will give use the gradient! Let’s draw a larger one.
In general, to find the gradient of a straight line, we divide the…
vertical change by the…
horizontal change.
The gradient, m = 2/4 = ½ 2
y = ½x - 2
y = mx +c 4

7. Plenary: Assessing ourselvesx 1 2 3 4 5 6 7 8
–7 –6 –5 –4 –3 –2 –1 -1 -2 -3 -4 -5 -6
y = 2x + 4
y = 2x - 3
y = 3x + 2
y = -2x + 6
y = x + 3
y = 4
y = 4x + 2
y = -x + 2
x = 2

8. Did you meet the objective?
Understand that all straight line graphs can be represented in the form y=mx+c, and be able to state the equation of given graphs