Transcript The equation of a straight line graph

Drawing Graphs
from Equations
Sunday, 03 April 2016
A graph can be drawn from an
equation.
For example, draw the graph of:
y = 2x + 1
This is the equation or
RULE for drawing the
12
11
This is the graph
of y = 2x + 1
x
0
2x
0
2x + 1 1
y
1
1
2
3
3
2
4
5
5
3
6
7
7
10
The y numbers
9
4
8
9
9
8
7
6
5
4
3
2
1
0
0
1
2
3
4
The x numbers
5
6
x
0
To draw the graph of
y = 2x + 1
draw a table like this
putting in the x numbers
0-4
1
2
3
4
x
0
1
2
3
4
2x
0
2
4
6
8
I want to find
y = 2x + 1, so first, you
find the value of the
2x. This means 2 X x so
times each of the x
numbers by 2.
x
0
1
2
3
4
2x
0
1
2
3
4
5
6
7
8
9
2x + 1
Remember, you want
to find y = 2x + 1 so
you add on 1 to the
2x to find the value
of 2x + 1
x
0
1
2
3
4
2x
0
1
1
2
3
3
4
5
5
6
7
7
8
9
9
2x + 1
y
You have done
everything to the x
number so now you
have found the y
number y = 2x + 1
x
0
1
2
3
4
2x
0
1
1
2
3
3
4
5
5
6
7
7
8
9
9
2x + 1
y
Now, plot the value
of x against the value
of y on the graph’s
axes.
x
0
1
2
3
4
2x
0
1
1
2
3
3
4
5
5
6
7
7
8
9
9
2x + 1
y
12
11
10
Join up
the points
with a
line
The y numbers
9
8
7
6
5
4
3
2
1
0
0
1
2
3
4
The x numbers
5
6
0
1 2 3 4
2x
0
1
1
2 4 6 8
3 5 7 9
3 5 7 9
2x + 1
y
You can draw
any graph in a
similar way.
12
y= 2x + 1
11
10
9
The y numbers
x
8
7
6
5
4
3
2
1
0
0
1
2
3
4
The x numbers
5
6
Draw the graph of: y = 3x - 5
0
1
2
x
To draw the graph of
y = 3x - 5
draw a table like this putting
in the x numbers 0 - 4
3
4
Draw the graph of: y = 3x - 5
0
1
2
x
3x
0
Find the value of
3x. You times all
the x numbers
by 3.
3
6
3
4
9
12
Draw the graph of: y = 3x - 5
0
1
2
x
3x
3x - 5
0
-5
Take away 5
from the value
of 3x.
3
-2
6
1
3
4
9
4
12
7
Draw the graph of: y = 3x - 5
0
1
2
x
3x
3x - 5
y
0
-5
-5
You have done
all that the rule
asks so you have
the y value.
3
-2
-2
6
1
1
3
4
9
4
4
12
7
7
Draw the graph of: y = 3x - 5
x
3x
3x - 5
0 1 2
0 3 6
-5 -2 1
3
9
4
4
12
7
y
-5 -2 1
4
7
Plot the
points
y values
y = 3x - 5
8
7
6
5
4
3
2
1
0
-1 0
-2
-3
-4
-5
-6
1 2
3 4
x values
5
Draw the graph of: y = 3x - 5
y = 3x - 5
x
3x
3x - 5
0 1 2
0 3 6
-5 -2 1
3
9
4
4
12
7
8
y
-5 -2 1
4
7
4
7
6
5
y values
3
Join up the
points with
a straight
line
2
1
0
-1
0
1
2
3
-2
-3
-4
-5
-6
X values
4
5
Draw the graph of y = 6 – 2x
x
0
Draw a chart
with x values
0 to 4
1
2
3
4
Draw the graph of y = 6 – 2x
x
0
1
2
3
4
2x
0
2
4
6
8
Find the
value of 2x
Draw the graph of y = 6 – 2x
x
0
1
2
3
4
2x
0
6
2
4
4
2
6
0
8
-2
6 – 2x
Take 2x
away from
6
Draw the graph of y = 6 – 2x
x
0
1
2
3
4
2x
0
6
6
2
4
4
4
2
2
6
0
0
8
-2
-2
6 – 2x
y
You have done all that the rule
asks so you have the y value.
Draw the graph of y = 6 – 2x
y = 6 - 2x
x
0
1
2
3
4
7
2x
0
2
4
6
8
6
6 – 2x
y
6
6
4
4
2
2
0
0
-2
-2
5
4
Now, you can plot
the points and
draw the graph.
y values
3
2
1
0
-1 0
1
2
3
-2
-3
x values
4
5