20/11/2019
WALT:
Grad. & Intercept
Understand that linear functions in the form y=mx+c represent a
straight line.
WILF:
Is the answer to:
Is the answer to:
Write down the gradient
and y-intercept for the
linear function
Write down the gradient
and y-intercept for the
linear function
y = 3x – 1
y = 3x – 1
Keywords
Level 6
1 of 52
Gradient
Level 6
Y-intercept
Level 6
Is for youto:
find the function of a
straight line from a graph
Level 7
y
8
y  2x  8
7
y  2x  4
y  2x
6
Here are 4 equations:
y = 2x
y = 2x + 8
y = 2x + 4
y = 2x – 6
The equations have been plotted on the graph to the
left.
5
4
3
y  2x  6
2
Looking at all equations and all the corresponding
graphs. Write down some observations you have made
(what is similar/ what is different/ how do the graphs link to the
equations).
1
-4 -3 -2 -1
-1
-2
-3
-4
-5
-6
-7
-8
2 of 52
1
2
3
4
x
...........................................................
...........................................................
...........................................................
...........................................................
...........................................................
...........................................................
...........................................................
...........................................................
y
8
y  4x 1
y  2x 1
7
6
Here are 4 equations:
y = 2x + 1
y = -x + 1
y = 4x + 1
y = ½x + 1
The equations have been plotted on the graph to the
left.
5
4
3
y
2
Looking at all equations and all the corresponding
graphs. Write down some observations you have made
1
x  1 (what is similar/ what is different/ how do the graphs link to the
2
equations).
1
-4 -3 -2 -1
-1
1
2
3
4
x
-2
-3
-4
-5
-6
-7
-8
3 of 52
y  x 1
...........................................................
...........................................................
...........................................................
...........................................................
...........................................................
...........................................................
...........................................................
...........................................................
20/11/2019
Grad. & Intercept
Definition
The general equation of a straight line can be written as:
y = mx + c
The value of m tells us the gradient of the line.
The value of c tells us where the line crosses the y-axis.
This is called the y-intercept and it has the coordinate (0, c).
For example, the line y = 3x + 4 has a gradient of 3 and crosses the yaxis at the point (0, 4).
4 of 52
20/11/2019
Gradient:
Grad. & Intercept
M stands for the gradient
5
5
4
4
3
3
2
2
1
1
0
0
0 1 2 3 4 5
m=1
5 of 52
5
4
3
2
1
0
0 1 2 3 4 5
0 1 2 3 4 5
m=3
m=½
Grad. & Intercept
20/11/2019
Y- Intercept:
C stands for the Intercept
-1
-2 -1
-2
1 2 3
c=2
6 of 52
3
2
1
3
2
1
3
2
1
-1
-2 -1
-2
1 2 3
c=0
-1
-2 -1
-2
1 2 3
c = -1
20/11/2019
Example:
Grad. & Intercept
Find the Gradient and y intercept of these linear functions.
a) y =3x – 4
Gradient
=2
Y-intercept
=1
b) y = ½x + 5
Gradient
=½
Y-intercept
=5
7 of 52
20/11/2019
Grad. & Intercept
Exercise 1:
Complete this table:
8 of 52
equation
gradient
y = 3x + 4
3
4
x
y=
–5
2
1
2
–5
y = 2 – 3x
–3
2
y=x
1
0
y = –2x – 7
–2
–7
y-intercept
20/11/2019
Example:
Grad. & Intercept
Find the Gradient and y intercept of these lines.
6
6
Gradient
=2
4
-2
4
Y-intercept
=1
2
2
4
6
-2
2
-2
-4
-4
9 of 52
Y-intercept
=3
2
-2
y=2x + 1
Gradient
= -3
4
y=-3x + 3
6
Grad. & Intercept
20/11/2019
Exercise 2:
Name the function for each line.
E
B
A
C
y 14
12
10
8
6
F
4
2
-8
-6
-4
-2
-2
-4
-6
10 of 52
2
4
6
8
x
D
a
x=3
b
y = 3x - 3
c
y=x+4
d
y = -2
e
y = -2x + 9
f
y = -½x - 1
20/11/2019
Example:
Grad. & Intercept
Draw these linear functions
Gradient
=2
6
4
Y-intercept
=-2
2
-2
2
-2
-4
11 of 52
y=2x - 2
4
6
20/11/2019
Grad. & Intercept
Exercise 3:
Draw the following graphs without a table of values
X-axis from -2 to 4 and the y-axis from -10 to 10
1
2
3
4
12 of 52
y = 2x
5
y = ½x - 9
y = 2x + 3
6
y = -x + 6
y = 4x -1
7
y = -2x
y = 3x - 4
7
y = -3x - 2
20/11/2019
WALT:
Grad. & Intercept
Understand that linear functions in the form y=mx+c represent a
straight line.
WILF:
Is the answer to:
Is the answer to:
Write down the gradient
and y-intercept for the
linear function
Write down the gradient
and y-intercept for the
linear function
y = 3x – 1
y = 3x – 1
Keywords
Level 6
13 of 52
Gradient
Level 6
Y-intercept
Level 6
Is for youto:
find the function of a
straight line from a graph
Level 7
y
8
y  2x  2
Here is the line y = 2x + 2
7
6
1) Move the line y = 2x + 2 two places to the right
5
4
2)
Write the equation of the new line
3
________________________
2
1
-4 -3 -2 -1
-1
1
2
3
4
3)
Move the line y = 2x + 2 three places to the left
4)
Write the equation of the new line
x
-2
-3
-4
-5
-6
-7
-8
14 of 52
_________________________