1+1=2
It’s been proven, it’s always true.
Let’s add some letters to represent the unknown.
Now 1x+1y=2
Please explain how?
This is a linear equation,
When we rearrange its formation.
Now let’s put it in standard notation.
Ax+By+C=0
1x+1y-2=0
What does this mean?
It’s an equation for a graph where the constant is always C.
Now to find a slope for our graph,
We must yet again rearrange to get y=mx+b;
Where ‘m’ equals the slope that we need.
1x+1y-2=0
1y=-1x+2
m=-1
Lets not forget m is also rise over run!
The rise equals ‘∆y’ and the run ‘∆x’.
If you have 2 exact points you can also use them to find ‘m’.
Now the average rate of change is much like the slope.
It is derived from the same formula but now we must develop.
Instead of simple digits we are presented graphical expressions.
We must calculate the average rate of their alterations.
A secant line would be helpful to move further.
A secant line is a line from one point to another.
By calculating the slope of this secant line,
We will have the average rate of change between two periods of time.
Can there be a rate for an exact time?
Of course and that is called the instantaneous rate of change.
Instead of a secant line we shall use a tangent.
Up against the point it will give an approximation.
The x values will be so close,
It will create a limit of ‘x’ approaching 0.
Don’t be quick to leave there is still more.
The difference quotient is an expression,
To find the slope of a secant line between two specifications.
This expression is then used to find,
The instantaneous rate of change or the average rate of change over a period of time.
I don’t mean to scare you,
But this is just the beginning of chapter 1.2.
Feb 18, 2013
Feb 18, 2013 at 11:35 PM UTC
1+1=2
It’s been proven, it’s always true.
Let’s add some letters to represent the unknown.
Now 1x+1y=2
Please explain how?
This is a linear equation,
When we rearrange its formation.
Now let’s put it in standard notation.
Ax+By+C=0
1x+1y-2=0
What does this mean?
It’s an equation for a graph where the constant is always C.
Now to find a slope for our graph,
We must yet again rearrange to get y=mx+b;
Where ‘m’ equals the slope that we need.
1x+1y-2=0
1y=-1x+2
m=-1
Lets not forget m is also rise over run!
The rise equals ‘∆y’ and the run ‘∆x’.
If you have 2 exact points you can also use them to find ‘m’.
Now the average rate of change is much like the slope.
It is derived from the same formula but now we must develop.
Instead of simple digits we are presented graphical expressions.
We must calculate the average rate of their alterations.
A secant line would be helpful to move further.
A secant line is a line from one point to another.
By calculating the slope of this secant line,
We will have the average rate of change between two periods of time.
Can there be a rate for an exact time?
Of course and that is called the instantaneous rate of change.
Instead of a secant line we shall use a tangent.
Up against the point it will give an approximation.
The x values will be so close,
It will create a limit of ‘x’ approaching 0.
Don’t be quick to leave there is still more.
The difference quotient is an expression,
To find the slope of a secant line between two specifications.
This expression is then used to find,
The instantaneous rate of change or the average rate of change over a period of time.
I don’t mean to scare you,
But this is just the beginning of chapter 1.2.
This goes out to Advance Functions and Calculus and Vectors; you are taking over my life.