Massey logo
Home > College of Sciences > Institute of Fundamental Sciences >
Maths First > Online Maths Help > Algebra > Linear Equations and Graphs > Finding Points on a Line
SEARCH
MASSEY
MathsFirst logo College of Science Brandstrip
  Home  |  Study  |  Research  |  Extramural  |  Campuses  |  Colleges  |  About Massey  |  Library  |  Fees  |  Enrolment

 

Linear Equations and Graphs

Background

We assume that you are familiar with the Cartesian coordinate system and solving linear equations.

Functions which have straight line graphs are called linear functions (for the obvious reason). These functions can always be written in the form

y=m*x+b

(To see why click here.) The set of points given by the ordered pairs that satisfies the above equation is a straight line.

 

Finding Points on a Line

To find points on the line y = mx + b,

  • choose x and solve the equation for y, or
  • choose y and solve for x.

Example 1.

Find two points on the line y = 2x + 1:

Point 1 - Choose x and solve for y:

Let x =1. Substitute x = 1 into y = 2x + 1 and solve for y.

y = 2(1) + 1 = 2 + 1 = 3

Hence (1,3) is one point on the line y = 2x + 1.


Point 2 - Choose y and solve for x:

Let y = -3. Substitute y = -3 into y = 2x + 1 and solve for x.

-3
=
2x + 1 (Subtract 1 from both sides)
-4
=
2x (Divide both sides by 2)
-2
=
x  

Hence (-2,-3) is another point on the line y =2x+1.

 

Exercise 1.

Follow the above example and try some of the following exercises:

Locate points on the line defined by y = x +

 

x
y

 

 

 

Linear Equations and Graphs Index | The Graph of a Linear Function (Drawing a Graph Using 2 Points) >>

 

   Contact Us | About Massey University | Sitemap | Disclaimer | Last updated: November 21, 2012     © Massey University 2003