Algebra/Point-Slope

Date: 01/09/98 at 09:36:36
From: Lee Phillips
Subject: Algebra/Point-Slope

I don't understand how to do point-slope equations. Can you explain 
them?

Date: 01/12/98 at 13:02:01
From: Doctor Loni
Subject: Re: Algebra/Point-Slope

The point slope form of an equation is just one of many ways to write 
the equation of the line. It's handy to use when you know the slope of 
a line and one point on it.

A point-slope equation looks like this:

       y - y1 = m (x - x1)

where m is the slope and x1 and y1 correspond to a point on the line.  

In order to solve a problem (that is, write an equation of a line)  
using the point-slope equation you need two things: a point on the 
line (x, y), and the slope of the line.

For example, to find the equation of a line with a slope of 2 and a 
point on the line (-1, 3):  

   m would be equal to 2; x1 would be -1 and y1 would be 3.  

Plugging them into the point slope equation  you get:

     y - 3 = 2 (x - (-1))   

Then solve for y to simplify the equation.

Sometimes you will get a problem that says to write the equation of 
the line, but you are only given two points and you are not given the 
slope. For example, find the equation of the line that contains the 
points (2,1) and (0,-1). In order to use the point-slope form of the 
equation you need to find the slope (m), which is the difference in 
the y coordinates divided by the difference in the x coordinates (i.e. 
rise over run):

      m = (y2-y1)/(x2-x1)

Putting in the numbers you would get

      m = (-1 - 1)/(0 - 2) = -2/-2 = 1

Therefore the slope of the line is 1.

Using the slope and one of the points you were given (it doesn't 
matter which one) you can use the point slope formula: (I'll use the 
first point given):

      y - 1 = 1 (x - 2) 

Solve for y to simplify.

I hope this helps!  If you have another question or this question 
didn't quite get at what you needed, please let us know.

-Doctor Loni,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   

Date: 01/15/98 at 14:19:56
From: Becky Phillip
Subject: Re: Algebra/Point-Slope

Thank you so much.  You helped me alot!