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Some Basic Algebraic Functions: Linear function

Graphing a linear function

A graph of an equation in two variables is the set of all points that satisfy the equation.

If you’re given the equation y = 3x-2 and asked to graph it, you would do the following steps. (Note: This equation is a linear equation, which means it will appear as a straight line). The first step is to set up a table of x and y.

y = 3x-2                     

    x    

    y    

    0

   -2

   1

   1

   2/3

   0

Assign values to x, then figure out what the value for y will be. For example, if x = 0, then y = -2. If x = 1 then, y = 1, and if x=2/3, then y = 0. Note that it’s good to choose x=0 and y = 0 because x intersects the y-axis when it has the value of 0, and y intersects the  x–axis when it has the value of 0.

From the table above, we have the points (0, -2), (1, 1) and (2/3, 0). However, to draw a line you would only need to plot two points and then connect those dots. Since "linear" equations produce a straight line, you might as well use your ruler for this part.

You can see in the graph below these points are connected in a straight line.

 

 

Press the "Play Button" on navigation bar to see the steps.

Definition

linear function could be written in the following standard equation y = f(x) =  bx+ a. So, a linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.  The highest power over the x variable  in a linear function is 1.

Example:  y = 2x-1  is a straight-line equation, where b=2 and a= -1. 

 

Exercise. Drag Point A and explore how line-equation changes.

  • How does the line look when "b" is positive?
  • How does the line look when "b" is negative?
  • What is the relation between coordinates of  point "A"  and the line equation?
  • What is the line equation when you place "A" on the origin"?
  • What position does the line take when  the line equation changes to y=a (notice that there is no x variable in the equation)?  How does the line look (parallel to what axis)?

 

 

Credits

Created by peer tutors under the direction of Learning Centre faculty at Douglas College, British Columbia.

 

Project Coordinator and LibGuide developer

 Mina Sedaghatjou

 

 

 

 

 

 

 

 

 

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