Linear Function

Hi my name is Marwa,

Today I’m going to take about (linear function): few questions come to mind when we say linear function.

1. What is a linear function?

      It is a function with a single variable that make a graph of a line.

2. Why do we study the linear function?

      To create an approximate line that can include the most into out of a real life               situation.

3. What makes it linear?

     The slope which is (the change of Y over the change of X) of the function, so in      order to be a linear function the slope of all of X and Y have to be constant.

There are three formulas to find the linear function:

A)  If we have the y-int and a point (x,y), we can use the slope –intercept formula :

       

y=mx+b

when : m=(y2-y1)/(x2-x1)

               b= y-int.

B)  If we have the slope and a point (x,y), we can use the point-slope formula:

y-y1= m(x-x1)

 when : (x1,y1) is the point that we have to use in the formula.

               m=(y2-y1)/(x2-x1)

C) The standard formula:  Ax+By=C

Note:

v We can have a horizontal line: y=b and that’s when the change of y equal zero that makes the slope=0

                                                      Slope = m= (0/x2-x1)=0

v As we can also have a vertical line: X=a  and that’s when the change of X equal zero that makes the slope undefined.

                                    Slope=m=(y2-y1)/0=undefined

Example:

x	F(x)
0	10
5	20
10	30
15	40

Y-int: when x=0, (0,10)

Slope=m= (y2-y1)/(x2-x1)

                     (20-10)/(5-0)=2

                     (30-20)/(10-5)=2

                     (40-30)/(15-10)=2              So, m=2

So by testing the slope of all the pointes, we got the same slope throw the whole table.

Now we can write our linear function in the slope- intercept formula

Y=2x+10