document.write( "Question 613594: What 2 things do we need to write the equation of a line ? \n" ); document.write( "
Algebra.Com's Answer #386118 by Theo(13342)\"\" \"About 
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you need a minimum of either:
\n" ); document.write( "(a) 1 point on the line and a slope
\n" ); document.write( "(b) 2 points on the line
\n" ); document.write( "from 2 points on the line, you can calculate the slope and then, using one of the points, can determine the equation.
\n" ); document.write( "equation for a straight line is:
\n" ); document.write( "(a) standard form:
\n" ); document.write( "ax + by = c
\n" ); document.write( "(b) slope intercept form:
\n" ); document.write( "y = mx + b
\n" ); document.write( "(c) point slope form:
\n" ); document.write( "y-y1 = m(x-x1)
\n" ); document.write( "m is the slope
\n" ); document.write( "b is the y-intercept
\n" ); document.write( "m can be determine by the equation of:
\n" ); document.write( "m = (y1-y2)/(x1-x2)
\n" ); document.write( "(x1,y1) is one point on the line.
\n" ); document.write( "(x2,y2) is the other point on the line.
\n" ); document.write( "once you know the slope, you can use either the point slope form or the y intercept form to generate the equation of the line.
\n" ); document.write( "example:
\n" ); document.write( "2 points are (1,5) and 2,7)
\n" ); document.write( "assign (1,5) to be (x1,y1) - you can assign either one of the points - it doesn't matter.
\n" ); document.write( "assign (2,7)) to be (x2,y2) - this is the other point.
\n" ); document.write( "from those 2 points, find the slope.
\n" ); document.write( "m = (y1-y2)/(x1-x2) = (5-7)/(1-2) = -2/-1 = 2
\n" ); document.write( "slope intercept form of the equation becomes:
\n" ); document.write( "y = 2x + b
\n" ); document.write( "substitute either point for x and y and solve for b.
\n" ); document.write( "b is the y-intercept.
\n" ); document.write( "example:
\n" ); document.write( "use the point (2,7)
\n" ); document.write( "slope intercept form of the equation becomes:
\n" ); document.write( "7 = 2(2) + b which becomes:
\n" ); document.write( "7 = 4 + b which becomes:
\n" ); document.write( "b = 3
\n" ); document.write( "slope intercept form of the equation becomes:
\n" ); document.write( "y = 2x + 3
\n" ); document.write( "you could also have used the point slope form of the equation once you knew that m = 2
\n" ); document.write( "point slope form of the equation is y-y1 = m(x-x1) which becomes:
\n" ); document.write( "y-y1 = m(x-x1)
\n" ); document.write( "assign one of the points to (x1,y1) - it doesn't matter which one.
\n" ); document.write( "we'll use (1,5) = (x1,y1)
\n" ); document.write( "point slope form of the equation becomes:
\n" ); document.write( "y-5 = 2(x-1)
\n" ); document.write( "we can now convert this to slope intercept form by solving for y as follows:
\n" ); document.write( "add 5 to both sides of the equation to get:
\n" ); document.write( "y = 2(x-1) + 5 which becomes:
\n" ); document.write( "y = 2x-2 + 5 which becomes:
\n" ); document.write( "y = 2x + 3
\n" ); document.write( "same equation as before only we derived it a different way./
\n" ); document.write( "to get to the standard form of the equation, start from the slope intercept form of the equation and manipulate to the standard form as shown below:
\n" ); document.write( "y = 2x + 3
\n" ); document.write( "subtract 2x from both sides of the equation to get:
\n" ); document.write( "-2x + y = 3
\n" ); document.write( "you can leave it like this or you can multiply both sides of the equation by -1 to make the x term positive.
\n" ); document.write( "if you do, then you get:
\n" ); document.write( "2x - y = -3
\n" ); document.write( "either form is acceptable.
\n" ); document.write( "all forms of the equation for the same straight line can be derived from either form with a little algebra.\r
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