This post was contributed by a community member. The views expressed here are the author's own.

Health & Fitness

Finding equation of a line (Algebra 1)

Mathnasium - Math Learning Center's profile picture
Mathnasium - Math Learning Center, Neighbor

One of the topics that Algebra 1 student will be asked to do is to find an equation of a line.  This is the first introductory question which will later evolve into solving system of (2 or 3) linear equations. 

Different variations of this type of question include:

  1. Given a slope (m = 1/2) and given a point that the lines passes through (1,2)
  2. Given 2 points (3,4) and (1,2) and they are part of the line
In order to solve question #1, you will utilize the slope intercept form of the equation (y = mx + b).  You are already given the value of the slope (m = 1/2), so all you will need to do is to solve for the y intercept of the line (b).

y = mx + b
y = 1/2x + b  (at this point, you will substitute the point (1,2) into the equation, since this point exist on the line)

2 = 1/2(1) + b
3/2 = b

So the equation for question #1 is

y = 1/2x + 3/2

In order to find the equation of the line for question #2, you will first need to determine the slope of the line first.  Once you have the slope of the line, you can just repeat the process like question #1, and find the equation.

The definition of the slope of the line is m = rise/run = (y1 - y2)/(x1 - x2).  We will assume (x1,y1) = (3,4) and (x2,y2) = (1,2). 

m = (4-2)/(3-1) = 2/2 = 1

A classic question that students wonder is does it matter if I evaluate the slope of the line using other points on the same graph?  The answer is NO!  Since it is a linear line, it does not matter which points you use to find the slope of the line.  The slope of the line WILL always be the same.  Let's prove it by making the points to be (x1,y1) = (1,2) and (x2,y2) = (3,4). 

m = (2-4)/(1-3) = -2/-2 = 1

As you can see, I can take any 2 points on the line to find the slope.  Once you have found the slope of the line, question #2 actually becomes exactly like question #1.  You now have the slope of a line (m = 1), and you are given 2 points (3,4) and (1,2) to find the equation of the line.  You can use any of the 2 points to find the equation.

Using point (3,4)
y = mx + b
4 = 1(3) + b
b = 1

Therefore the equation of this line is y = 1x + 1 = x + 1.

If you have any question regarding this type of problems, please feel free to reach out to me or any of the instructors in my center.

Michael Huang
Center Director
Mathnasium of Glen Rock/Ridgewood
T:     201-444-8020   
E:  glenrock@mathnasium.com
www.mathnasium.com/glenrock




The views expressed in this post are the author's own. Want to post on Patch?

More from Ridgewood-Glen Rock