document.write( "Question 158780: How do i find the equation of a line, for example a line through points (1,-6) and (4,3). I have no idea how to find the equation, thanx to a few absences. \r
\n" ); document.write( "\n" ); document.write( "Thank you,\r
\n" ); document.write( "\n" ); document.write( "John \n" ); document.write( "
Algebra.Com's Answer #116948 by gonzo(654)\"\" \"About 
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if the line goes through (1,-6) and (4,3), then the x coordinates are 1 and 4, and the y coordinates are -6 and 3.
\n" ); document.write( "let x1 = 1,
\n" ); document.write( "let y1 = -6
\n" ); document.write( "let x2 = 4
\n" ); document.write( "let y2 = 3
\n" ); document.write( "slope-intercept form of the equation would be y = m*x + b where m is the slope and b is the y-intercept when x = 0.
\n" ); document.write( "formula for slope is (y2-y1)/(x2-x1)
\n" ); document.write( "this equals (3-(-6))/(4-1) which equals 9/3 which equals 3.
\n" ); document.write( "the slope of the equation = 3 = m
\n" ); document.write( "so the slope-intercept form of the equation is y = 3*x + b
\n" ); document.write( "to find b, you need to solve the equation for one of the points given.
\n" ); document.write( "take (1,-6)
\n" ); document.write( "this makes y = 3*x + b equal to -6 = 3*1 + b
\n" ); document.write( "this makes b = -9.
\n" ); document.write( "y-intercept form of the equation is therefore y = 3*x-9
\n" ); document.write( "substituting in the other set of points of the line, we get
\n" ); document.write( "3 = 3*4-9 = 12-9 = 3 which means the equation is good because we have an identity.
\n" ); document.write( "so you have the y-intercept form of the equation is y = 3*x-9.
\n" ); document.write( "to transform this to the standard form of the equation, we need to make it look like a*x + b*y = c where a,b,c are constants.
\n" ); document.write( "subtracting 3*x from both sides of the equation gets
\n" ); document.write( "-3*x + y = -9
\n" ); document.write( "since this satisfies the form of the standard equation we can stop here.
\n" ); document.write( "solving for one of the points, we use (1,-6) and we get
\n" ); document.write( "-3*1 + (-6) = -9 which becomes
\n" ); document.write( "-3-6=-9
\n" ); document.write( "which becomes
\n" ); document.write( "-9=-9 proving the standard form of the equation is accurate.
\n" ); document.write( "you have 2 forms of the same equation
\n" ); document.write( "y = 3*x-9 is the slope-intercept form.
\n" ); document.write( "-3*x+y=-9 is the standard form.\r
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