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
y are the co-ordinates?
Starter: What
(-4, -2)
(4,(-1,
6) 1)
(6,(5,
(4,
-2)
5)3)
(2,
-3)
(3,(7,
2)1)
(-2,
-4)2)
(1,(-7,
5)
(-4,
3)-1)
(-2,
8
7
6
5
4
3
2
1
–7 –6
–5 –4 –3
–2 –1
-1
1
2
3 4
5
6
7 8
x
-2
-3
-4
-5
-6
Skip Starter
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!
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”.
Look at the straight line.
y and c
Finding m
6
It is very easy to find
the value of c – this is
the point at which the
line crosses the
y-axis
5
So c = 3
8
7
4
3
2
1
–7 –6
–5 –4 –3
–2 –1
-1
1
2
3 4
5
-3
-5
-6
7 8
x
Each time the lines
moves 1 place to the
right, it climbs up by 2
places.
-2
-4
6
Finding m is also
easy in this case. The
gradient means the
rate at which the line
is climbing.
yy == mx
2x +3
+c
So m = 2
We can see that c = -2
Another yexample
As the line travels
across 1 position, it is
not clear how far up it
has moved.
8
7
But… Any right angled
triangle will give use the
gradient! Let’s draw a
larger one.
6
5
4
3
In general, to find the
gradient of a straight
line, we divide the…
2
1
–7 –6
–5 –4 –3
–2 –1
-1
1
2
3 4
5
-3
4
-6
change
x vertical
by the…
The gradient, m = 2/4 = ½
-4
-5
7 8
horizontal change.
-2
2
6
y = mx
½x -+c
2
Plenary: Assessing ourselves
y
y = 2x + 4
y = 2x - 3
y = 3x + 2
8
7
6
5
4
3
2
1
–7 – 6
–5 –4 –3
–2 –1
-1
-2
-3
-4
-5
-6
1
2
3 4
5
6
7 8
x
y = -2x + 6
y=x+3
y=4
y = 4x + 2
y = -x + 2
x=2