To find the equation of a line you need to know either two points or one point and the slope. If you are given two points, the first step in any of the methods is to find the slope from the two given points. So first memorize the slope formula.
Given: A line passes through the two points (-4, 1) and (2, 5). Find an equation of this line.
Finding the Slope
All three methods require the slope of the line, so first find the slope:
Note: Either point may be considered ( x1 , y1 ) Point-Slope Method
Plug in the slope for m, and either of the given points for ( x1, y1 ). So here we are finding the equation of a line with slope 2/3 passing through the point (2, 5).
Then convert to standard form:
Eliminate denominator
Rearrange terms 
Change signs, done! 
The standard form equation is 
Slope-Intercept Method
Plug in the slope for m, and either of the given points for ( x, y ). This time we'll use the other point, so here is the method for finding the equation of a line with slope 2/3 passing through the point (-4, 1).
Now solve for b, and rewrite with x, y.
The slope-intercept equation is 
Converting between Forms
The previous methods are all that is ever needed. It is helpful to have a shortcut, or quick method, but not necessary. Before you ever apply the third method you should be able to easily convert between the standard and slope-intercept forms of linear equations.
Converting to Slope-Intercept Form
Converting to slope-intercept from standard form:
Add the opposite of the x-term to both sides, and if necessary divide by the coefficient of the y-term, and simplify.
a)  | b)  | c)  |
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Converting to Standard Form
Converting to standard from slope-intercept form: Multiply through by the LCD, if necessary, then move the x-term to the left side, and adjust the signs.
a)  | b)  | c)  |
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Study the examples above, and compare both forms. Look at the slope in slope-intercept form, and compare that with the left-hand side of the standard form.
Practice, and mastery of these conversions leads to the understanding that
Standard Form Shortcut
The shortcut is very simple: Create the left-hand side of a standard form equation with the given slope. Then find the value of the constant C by plugging in any given point. So, to find the equation of a line with slope 2/3 passing through the point (2, 5):
Slope 2/3
Plug in (2, 5)
Therefore, the standard form equation is 
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