 # 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 ﻿

## Fun collection of Math clips

Fun collection of Math in movies:

Mathematics in Movies