Drawing Graphs from Equations

1
Drawing Graphs from Equations
Monday, 21 June 2021
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 graph
2
This is the graph of y 2x 1
x 0 1 2 3 4
2x 0 2 4 6 8
2x 1 1 3 5 7 9
y 1 3 5 7 9
3
x 0 1 2 3 4



To draw the graph of y 2x 1 draw a table
like this putting in the x numbers 0 - 4
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.
5
x 0 1 2 3 4
2x 0 2 4 6 8
2x 1 1 3 5 7 9

Remember, you want to find y 2x 1 so you add
on 1 to the 2x to find the value of 2x 1
6
x 0 1 2 3 4
2x 0 2 4 6 8
2x 1 1 3 5 7 9
y 1 3 5 7 9
You have done everything to the x number so now
you have found the y number y 2x 1
7
x 0 1 2 3 4
2x 0 2 4 6 8
2x 1 1 3 5 7 9
y 1 3 5 7 9
Now, plot the value of x against the value of y
on the graphs axes.
8
x 0 1 2 3 4
2x 0 2 4 6 8
2x 1 1 3 5 7 9
y 1 3 5 7 9
Join up the points with a line
9
x 0 1 2 3 4
2x 0 2 4 6 8
2x 1 1 3 5 7 9
y 1 3 5 7 9
y 2x 1
You can draw any graph in a similar way.
10
Draw the graph of y 3x - 5
x 0 1 2 3 4



To draw the graph of y 3x - 5 draw a table
like this putting in the x numbers 0 - 4
11
Draw the graph of y 3x - 5
x 0 1 2 3 4
3x 0 3 6 9 12


Find the value of 3x. You times all the x numbers
by 3.
12
Draw the graph of y 3x - 5
x 0 1 2 3 4
3x 0 3 6 9 12
3x - 5 -5 -2 1 4 7

Take away 5 from the value of 3x.
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Draw the graph of y 3x - 5
x 0 1 2 3 4
3x 0 3 6 9 12
3x - 5 -5 -2 1 4 7
y -5 -2 1 4 7
You have done all that the rule asks so you have
the y value.
14
Draw the graph of y 3x - 5
x 0 1 2 3 4
3x 0 3 6 9 12
3x - 5 -5 -2 1 4 7
y -5 -2 1 4 7
Plot the points
15
Draw the graph of y 3x - 5
x 0 1 2 3 4
3x 0 3 6 9 12
3x - 5 -5 -2 1 4 7
y -5 -2 1 4 7
Join up the points with a straight line
16
Draw the graph of y 6 2x
x 0 1 2 3 4



Draw a chart with x values 0 to 4
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Draw the graph of y 6 2x
x 0 1 2 3 4
2x 0 2 4 6 8


Find the value of 2x
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Draw the graph of y 6 2x
x 0 1 2 3 4
2x 0 2 4 6 8
6 2x 6 4 2 0 -2

Take 2x away from 6
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Draw the graph of y 6 2x
x 0 1 2 3 4
2x 0 2 4 6 8
6 2x 6 4 2 0 -2
y 6 4 2 0 -2
You have done all that the rule asks so you have
the y value.
20
Draw the graph of y 6 2x
x 0 1 2 3 4
2x 0 2 4 6 8
6 2x 6 4 2 0 -2
y 6 4 2 0 -2
Now, you can plot the points and draw the graph.