blog post 4 (Leah Sorini)-be the professor

Linear Functions 
A linear function is when the rate of change at every interval is the same (AKA constant) and the graph is in a straight line.


To the fine the rate of change of a function:
(Y2-Y1)/(X2-X1)
You should use this equation with at least three different sets of points to check if a function is linear. If you get the same answer for multiple points, then the function is linear.


Equations used with linear functions are:
y=mx+b-->slope-intercept form
y-y0=m(x-x0)-->point-slope form
Ax+Bx=C-->standard form
slope=rise/run


There are three ways to find the equation of a line;
1. you need the slope and y intercept
Example:
m=2
y intercept=(0,7)
y=2x+7

2. you need a point and the slope
(4,2)
m=2
y-y0=m(x-x0)
y-2=2(x-4)
y=2(x-4)+2
y=2x-8+2
y=2x-6

3. you need two points
(-2,3)
(2,-2)
(y2-y1)/(x2-x1)
=(-2-3)/(2-(-2))
=(-5/4)
y-3=(-5/4)(x-(-2))
y=(-5/4)x+(1/2)


EXAMPLE

ROC=(Y2-Y1)/(X2-X1)=
(4-3)/(4-3)=1/1=1
(3-2)/(3-2)=1/1=1
(2-1)/(2-1)=1/1=1

Slope-Intercept Form: y=mx+b
y=1x+0