A' Plotting graphs of linear equations

1
A. Plotting graphs of linear equations

• Plot the graph for the equation y 3x 4

Key words
For x values between 0 and 5.
Set up a table for x and y.
Substitute each value of x in the linear equation
to find its respective value of y.
x
3
5
4
3
2
1
0
5
4
2
1
0
y
7
13
4
10
16
19
y values are called dependent variables because
they are dependent on each value of x substituted
in to the equation.
y 3x 4
( )
4
7
10
13
16
19
2
y
22

• Plot the (x, y) coordinates
• on a suitable graph.

20

(5, 19)
y 3x 4
18
16

(4, 16)
x
5
4
3
2
1
0
14
y
7
10
13
4
16
19

(3, 13)
12
y 3x 4 Q How does the 4 in the equation
tie in with the graph drawn?
10
(2, 10)

8

(1, 7)
6
4

(0, 4)
2
A It indicates where the line crosses the y
axis.
x
0
1
2
3
4
5
3
Linear Equations
y
y x 2
The general equation for a line is y mx c
3
y x 1
y x - 1
2
The constant c indicates where a line crosses the
y axis. Also called the y intercept.
1
y x 0
x
0
3
1
2
-1
4
Linear Equations
y
The general equation for a line is y mx c
y 2x 0
3
y ½ x 0
2
The gradient m describes the rate of change in y
as x increases.
1
y 1x 0
x
0
3
1
2
y 0 x 0
Absorb mathematics The properties of straight
lines.
-1
y -1 x 0
5
B. Finding a linear equation.

• Find the equation for the sequence

Worth remembering
X y 0 4 1 7 2 10 3 13 4 16 5 19
The general equation for a line is y mx c
constant
Gradient of a line
Key words
We have to find these values
6
B. Finding a linear equation.

• Find the equation for the sequence

differences
X y 0 4 1 7 2 10 3 13 4 16 5 19
The general equation for a line is y mx c
3
3
Find the differences in y as x increases.
3
As x increases by 1, y increases by 3.
3
This difference gives the value for m in the
general equation.
3
m 3
y 3x c
7
B. Finding a linear equation.

• Find the equation for the sequence

differences
X y 0 4 1 7 2 10 3 13 4 16 5 19
The general equation for a line is y mx c
0
3
3
Q Is the equation y 3x ? Let x 0
3
3
y 3( )
0
3
A No, the tables shows that y 4 when x 0.
8
B. Finding a linear equation.

• Find the equation for the sequence

differences
X y 0 4 1 7 2 10 3 13 4 16 5 19
The general equation for a line is y mx c
3
1
When x 0, y c (constant)
3
3
As y 4 so c 4. So the equation is y 3x 4
3
3
Check when x 1. y 3x 4
( )
7