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Common Core Example: 8.EE.C.8
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
graph of identity function

Equation of a Line

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linear equation equation graphed

Define Linear Equation

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.
In this example the slope  or m =  2/3

The y-intercept or b = -2

Resulting in the  equation 
  •  y= 2/3x  -  2
Y intercept
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.
Remember the X axis runs horizontally and  the Y axis runs up and down or vertically.
Rise  2
Run 3
For additional help with Linear Equations visit  Slope of a Line

The formula for a linear equation is y= mx +b

y intercept
slope formula

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
​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.

Hi Welcome to MooMooMath. Today we are going to look at the basic equation of a line. We usually try to write the line in what is called y intercept form which is y equals mx plus b. The x and y are variables and the M stands for slope and we can remember this by M stands for mountains and mountains have slope and then b is your y intercept. So here is a line graph and the other thing you have to notice is that in a linear equation X is always to the first power. We don’t write it, we assume that there is a little 1 here so any time we have an X to the first power we know we have a linear equation. So next we are going to count our slope and this one has a 3 over 3 slopes (rise3, run 3) so that means we have a slope of 1. Now let’s look at another example and here is our Cartesian coordinate plane and we will draw a line. So I will write the equation Y=mx +b. Next I will underline all that I need to replace. I need to find m and I will need to find b so let’s count our slope. It looks like it goes up 2 and over 3 so my slope is 2/3 X. Now I need to find the intercept. Where does the line cross the Y axis? It goes up two but it is below the X axis so it is negative 2. So my final equation will be y= 2/3x -2 Here is a quick overview. The equation is y=mx + b m=the slope, b=the y intercept and x and y are variables. You take Y= ___ X = ____ and fill in m for the slope and y for the b intercept. So looking at this example the slope is 2 over 1 or 2 and the line intercepts at 2 so the equation will be Y = 2x + 2 Hope this video was helpful.