Equation of a Line
Date: 02/14/2002 at 00:32:12 From: Victor Squillacioti Subject: Proofs Prove the point-slope equation property, which is y-y1 = m(x-x1). It gave me a hint, but it wasn't very useful to me. It was: Show that any point (x2,y2) on the line described must satisfy the equation, and that any point satisfying the equation must be on the line described. Please give me any useful information to help me. Thank you in advance. Victor Squillacioti
Date: 02/14/2002 at 16:52:15 From: Doctor Peterson Subject: Re: Proofs Hi, Victor. To show that this is the equation of the line through (x1,y1) with slope m, you have to show two things: (1) every point on the line satisfies the equation; (2) every point that satisfies the equation is on the line. That is what the hint said. Now, what does it mean for a point to be on the line? Since we know the slope of the line, which means that the slope between any two points on the line has the value m, we can say that the slope between points (x1,y1), which is given as on the line, and the point (x2,y2) which we are assuming is on the line, will be m. Write an equation that says this, and use that to show that the equation will be true when x = x2 and y = y2. You will have shown that (1) is true. Now to go the other way, suppose that you have a point (x2,y2) that satisfies the equation. Write out what the equation tells you about x2 and y2. You want to show that the slope between (x1,y1) and (x2,y2) is m, which will prove that (x2,y2) is on the line. Write out the definition of this slope, and see if you can show it is equal to m. Here is some information on the equations of a line that touches on this idea: Formulas for the Equation of a Line http://mathforum.org/dr.math/problems/michelle9.28.98.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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