Define Linear Equation

Common Core Example: 8.EE.C.8

linear equation is an equation that describes a straight line. One form of a linear equation is the slope intercept form which is written, y=mx +b. In this equation the m represents the slope of the line and the b represents the y intercept. 

For example, y= 4x + 3 means: the line has a slope of +4, and crosses the y intercept at 3. There are several forms of linear equations including, slope intercept form, point slope formula, and the standard form. A different forms allow you to describe the same line in different ways.

mthe slope, which is calculated by counting Rise over Run.
      
Slope can also be calculated using the slope formula, when you have two points on the line:
 
bthe y-intercept.  This is the point in which the line intercepts the y-axis.

Writing linear equations

Given a graph:
 
1.  Find the slope by counting rise or run
 
2.  Identify the y intercept (where the line crosses the y-axis)
 
3.  Plug in slope which is represented by m, and the y-intercept represented by  b, into the formula  y = mx + b

Different types of linear equations

Slope-intercept form: y=mx+b
-use when you have a graph or 
-when you have the slope and y-intercept
 
Point-slope form:    y-y1 = m(x-x1)
-use when you know the slope and one point
 
x1 and y1 are known points
m =slope
x and y are any other points on the line
 
Standard Form
Ax +By =C
A,B,C, are all numbers
Use when you want to graph. Use when you want know the x intercept.
For example y=2x-2
Rewrite 2x-y=2
A = 2
B= -1
C =2
 
Written as a function:
​A line can be written in function notation by replacing y with f(x).
f(x) = mx +b
Identity function:  f(x) =x
 
An identity function is used when your input equals your output.
 
Ex.  (1, 1), (-3, -3) or (100, 100)
 
This parent graph is a line with a slope of 1 and a y-intercept of 0.