Massey logo
Home > College of Sciences > Institute of Fundamental Sciences >
Maths First > Online Maths Help > Algebra > Linear Equations and Graphs > From a Line to the Equation (Linear Function)
SEARCH
MASSEY
MathsFirst logo College of Science Brandstrip
  Home  |  Study  |  Research  |  Extramural  |  Campuses  |  Colleges  |  About Massey  |  Library  |  Fees  |  Enrolment

 

Linear Equations and Graphs

Determining Linear Equations (or Functions) from Information about the Line

If we are given a straight-line graph, we can find the slope m and intercept b by direct measurement, and hence write down the equation. More usually, we are given some information about the line which allows us to calculate m and b and hence write the equation for the line. A linear function can be determined in the following cases:

  • Case 1: The slope and a point on the line are known.
  • Case 2: Two points on the line are given.

Example 6A.

Case 1: We are given the slope and a point and asked to find the equation of the line:

Suppose a line has the slope m = and passes through the point ( , ) .

 
Click on the step buttons to show how to find the linear function.

 

First substitute the slope into the equation of a line:

y = x + b

Next, substitute the point into the equation and solve for b:

= ( ) + b

Solving for b we find:          b =

y = x +

 

Example 6B.

Here we look at a special case of the above example where we are given the slope and the x-intercept. As the x-intercept defines a point, we again have the slope of a line and a point on the line and so we can find the linear function.

Let the slope of a line be   m = and x-intercept be   x =

Click on the step buttons to show how to find the linear function.

 

First substitute the slope into the equation of a line:

y = x + b

Next substitute the point ( , 0) into the equation:

= ( ) + b

                  Hence b =

y = x +

Note: If we are given the slope and the y-intercept, finding the equation of the line y = mx + b is straighforward as we have both m and b and can substitute these directly into the equation.

Exercise 6.

In the following exercise you are given the slope and one of the following: a general point on the line, the x-intercept or the y-intercept. Use the information given to determine the linear function.

Find the linear equation given any two of the following facts:

Slope
Point
x-intercept
y-intercept
Function
( , )
( , )
( , )
y = x +

Example 7.

Case 2: We are given two points and asked to find the equation of the line that goes through these two points:

If the line passes through ( , ) and ( , ),  then the slope of the line is  

 
-
 
m =
= to one decimal place.
 
-
 







Click on the step buttons to show how to find the linear function.


First substitute the slope into the equation of a line:

y = x + b

Next, substitute one of the two points into the equation and solve for b:

= ( ) + b

Hence b = to one decimal place.

y = x +

 

Exercise 7.

Find the linear equation given either two points or an x- and y- intercept:

Point
Point
x-intercept
y-intercept
Function
( , )
( , )
( , )
( , )
y = x +

 

Give your answers to 2 decimal places.


<< Graphing a Linear Function Using the Slope and y-Intercept | Linear Equations and Graphs Index | Linear Equations >>

 

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