Let's study Linear function !!

Prof. Fumi:
Hi everyone. I would like to introduce to you guys about Linear function today. Does  anyone know about Linear function is?

Students:
Linear function is a  function that it has the same rates of slope.

Prof. Fumi:
perfect! The characteristics of linear function have the same rates of change as well as the line is a straight line. The formula of a linear function is following y=ax+b. a is the slope and b is y-intercept. Slope can calculate in following: m=y1-y0/x1-x0. Y-interest is the number which cross the y-axis.

Let's do some exercise!  Here is the question,

Let's write a formula of this function.
First, is it linear function or not?

Student:
It is a linear function, because the slope is a straight line.

Prof. Fumi
Yes, but can you explain more specifically how to define it is linear?

Student:
 We can define whether the rate of slope is constant or not.  So pick up two points in this case (0,4) and (2, 0).  So, the line will be (0-4)/(2-0)=-4/2=-2 so the slope is -2. let's take other two points, (1, 2) and (3, -2) the slope will be (-2-2)/(3-1)=- -4/2= -2. These four points have same rate of slope therefore, it is linear function

Prof. Fumi
Good job!!!  Then, the slope is -2, so the formula will be y=-2x+b. Form the graph above, it can be easily recognazie the y-intercept is 4, but lets asume you only provide two points (0,4) and (2, 0). What will do?

Students: we can put   (0,4) into the equation. So it will be 4 =-2*0+b. b=4. y-intercept is 4 in this case.

Prof. Fumi
Yes, you got it!! So the equation will be y= -2x+4
This is the basic concepts of Linear function.

That's all for today!!