Linear Functions

What do you mean by linear?

very good !! very good !!

Linear function is a function of the form f(x) = mx+bWhere m and b are real numbers and m≠0. Domain: set of real numbers Range: set of real numbers

Some examples of linear function in different forms are the following:

Each of the form can be written in another form. For this purpose, the function form y=mx+b will be used synonymously as f(x)=mx+b, which suggests that y=f(x).

Example1: Rewrite each linear function in the form y=mx+b. Then determine the value of m and b.

Example1: Rewrite each linear function in the form y=mx+b. Then determine the value of m and b.

1. 4x-y=1m = ?b = ?

2. 2x+3y=6m = ?b = ?

y

Linear function can also be written in the form Ax+By=C. As an equation , this form is referred to as theLinear function can also be written in the form Ax+By=C. As an equation , this form is referred to as theSTANDARD FORM

Example2: Transform each linear function in STANDARD FORM.Example2: Transform each linear function in STANDARD FORM.

Example 3:T Determine if each is a linear function or not.Example 3:T Determine if each is a linear function or not.

SeatworkA. Transform each linear function into the form

y=mx+bA. Transform each linear function into the form y=mx+b

1.x+y=2 3. 5x+15y=32. 2x-y=5

B. Give the equivalent function in Standard FormB. Give the equivalent function in Standard Form

Assignment :

1.-3x+y=12. x-2y=63.4x-8y=34.-2x+12y=85.-3x-18y=15

A. Transform each linear function into the form y=mx+b

A. Transform each linear function into the form y=mx+b

B. Give the equivalent function in Standard Form

B. Give the equivalent function in Standard Form