10 December 2012
Drawing a line (basics)
There are three basic methods that one can use to draw a line in the xy-plane..
1. The table method:
This involves drawing up a table with x and y values.
2. The intercept method:
We find that x- and y-intercepts with this method.
3. The gradient and y-intercept method:
We use the y-intercept and the gradient.
Let's consider an example: y = 2x - 4
Remember the general formula for a line which is y = mx + c. In this case m represents the gradient and c represents the y-intercept.
The y-intercept is where the line intersects the y-axis on the xy-plane.
1. We choose some x values, say -2, -1, 0, 1, 2. We then substitute these values into the equation to obtain the corresponding values of y. We usually do this by drawing up a table to make it easier to see which x and y values correspond.
In our example, if x = 1, then y = -2, so we plot the point (1, -2) on the xy-plane. After plotting a few point you should be able to draw a straight line which goes through all the points.
2. We already know that c represents the y-intercept, which in our case is -4. So we know that (0, -4) is a point on the line. To find the x-intercept we let y = 0, then we find that x = 2. So (2, 0) is also a point on our line. Now we can draw a straight line through these two points and we should obtain the same line as with the first method.
3. We know that the y-intercept is -4. Also, m represents the gradient which is 2. The gradient is also known as the slope and can be found be considering the fraction y/x. So, if y/x = 2, this is the same as saying y/x = 2/1. Hence, we have the point (1,2) on our line, as well as (0,-4). Now we draw the straight line through these points.
1. The table method:
This involves drawing up a table with x and y values.
2. The intercept method:
We find that x- and y-intercepts with this method.
3. The gradient and y-intercept method:
We use the y-intercept and the gradient.
Let's consider an example: y = 2x - 4
Remember the general formula for a line which is y = mx + c. In this case m represents the gradient and c represents the y-intercept.
The y-intercept is where the line intersects the y-axis on the xy-plane.
1. We choose some x values, say -2, -1, 0, 1, 2. We then substitute these values into the equation to obtain the corresponding values of y. We usually do this by drawing up a table to make it easier to see which x and y values correspond.
In our example, if x = 1, then y = -2, so we plot the point (1, -2) on the xy-plane. After plotting a few point you should be able to draw a straight line which goes through all the points.
2. We already know that c represents the y-intercept, which in our case is -4. So we know that (0, -4) is a point on the line. To find the x-intercept we let y = 0, then we find that x = 2. So (2, 0) is also a point on our line. Now we can draw a straight line through these two points and we should obtain the same line as with the first method.
3. We know that the y-intercept is -4. Also, m represents the gradient which is 2. The gradient is also known as the slope and can be found be considering the fraction y/x. So, if y/x = 2, this is the same as saying y/x = 2/1. Hence, we have the point (1,2) on our line, as well as (0,-4). Now we draw the straight line through these points.
09 December 2012
08 December 2012
07 December 2012
The number 2
Even though 2 is such a small number, there are various properties illustrating the usefulness of this number.
First of all it is the second number in the natural number system.
It is an even number and also the only even number which is a prime number.
It helps us to determine whether an integer number is even, i.e. a number is even when it can be divided by 2.
The Roman numeral for 2 is II.
In some situations 2 can be called a couple or a pair, for instance two socks is called a pair of socks.
If we divide 100 by 2² we arrive at 25, the previous two number which I have discussed (see: The number 25, The number 100).
Being number 2, you can also say being second. In a medal race this would usually mean that you will receive the silver medal.
Number 2 is a fictional character in the Austin Power movies.
In terms of imaginary number we can write 2 as the product: 2 = (1+i)(1-i).
When we draw graphs we usually draw it in a 2-dimensional space, the xy-plane.
If you know of any other interesting facts, which I'm sure there are many of, please leave a comment.
First of all it is the second number in the natural number system.
It is an even number and also the only even number which is a prime number.
It helps us to determine whether an integer number is even, i.e. a number is even when it can be divided by 2.
The Roman numeral for 2 is II.
In some situations 2 can be called a couple or a pair, for instance two socks is called a pair of socks.
If we divide 100 by 2² we arrive at 25, the previous two number which I have discussed (see: The number 25, The number 100).
Being number 2, you can also say being second. In a medal race this would usually mean that you will receive the silver medal.
Number 2 is a fictional character in the Austin Power movies.
In terms of imaginary number we can write 2 as the product: 2 = (1+i)(1-i).
When we draw graphs we usually draw it in a 2-dimensional space, the xy-plane.
If you know of any other interesting facts, which I'm sure there are many of, please leave a comment.
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