What is a linear function?
A linear function is a function whose graph is a line. Here is an example:Your exercise: This is the graph of your function.

The graph of a linear function is always a line.
A similar word to linear function is linear correlation.
What is the slope of a linear function?
The slope of a linear function corresponds to the number in front of the x. It says how may units you have to go up / down if you go one unit to the right. Example:Your exercise: This is the graph of your function.

We see that this function has slope . If we go one square to the right of any point on the graph, we have to go two squares up to be on the graph again.
Another example, this time with negative slope:
Your exercise: This is the graph of your function.

This linear function has slope . This means whenever we go one square to the right, we have to go three squares down to be on the graph again.
What is the yline intercept of a linear function?
The yline intercept is the number at the end of the function. As the name says, it says where the function cuts the yaxis. If you take a look on the function graphs, you see that die yAchse bei schneidet und die yAchse bei schneidet.How to calculate the equation of the line from a point and the slope?
You have to insert the point into the equation, i.e. the one coordinate for x and the other one for f(x). Here is an example: Lets assume we know that our function has slope and goes through (25).Your exercise: Point (25); Slope 7; Your exercise: This is the graph of your function.
This is what Mathepower calculated: Calculate the yaxis intercept b by inserting: General form of the linear function: f(x)=mx+b Insert for m, for x and for f(x).
Therefore, the equation of the function is 
How to calculate the equation of a linear function from two given points?
First, we have to calculate the slope m by inserting the x and y coordinates of the points into the formula . This means: You calculate the difference of the ycoordinates and divide it by the difference of the xcoordinates. Here is an example:Your exercise: Point (12); Point (38); Your exercise: This is the graph of your function.
This is what Mathepower calculated: To calculate the slope m, use the formula
Calculate the yaxis intercept b by inserting: General form of the linear function: f(x)=mx+b Insert for m, for x and for f(x).
Therefore, the equation of the function is 
As we can see, the slope was calculated first. To find the equation of the function, you have to insert a point and get an equation which gives the yaxis intercept.