Linear Graphs

You could be intim­i­dated by graphs but I don’t think there’s any need. You just need to learn a few def­i­n­i­tions and prac­tice a few tech­niques to pick up some rel­a­tively easy marks.

Line Seg­ments and Mid-points

A graph paints a thou­sand words:

Line Segments and Mid-points

 

 

 

 

 

 

 

 

 

 

In exam­ples like the one above you can just use com­mon sense to find the mid-point of a line seg­ment like the one above but you can cal­cu­late the mid-point from just the co-ordinates of a line seg­ment with this formula:-

Formula to calculate the mid-point of a line segment

 

 

 

So, for exam­ple a line seg­ment AB has coordinates

A: (2, 10)
B: (10, 16)

What is the mid=point?

Using the for­mula from above, we have

Mid­point = ((2+10)÷2), ((10+16)÷2)

= (6, 13)

You can see this on a graph:-

Graph mid-point of line segment

 

Plot­ting Straight-Line Graphs

When you plot a lin­ear func­tion on a graph you get a straight line. A lin­ear func­tion is usu­ally expressed in the for­mat y= mx + b.

You can plot a lin­ear func­tion by feed­ing in val­ues of ‘X’ and cal­cu­lat­ing ‘Y’. In the­ory, because a lin­ear func­tion will result in a straight line you only need two sets of coor­di­nates. Nor­mally you will be asked to cal­cu­late a few sets of coor­di­nates in a table and then plot the line.

For exam­ple; draw the graph of y = 3x + 3 for val­ues of x from –3 to +3

Just 3 sim­ple steps; draw up a table, cal­cu­late the val­ues of y and plot the graph:

Table of Val­ues and Graph of Lin­ear Func­tion y = 3x + 3

Plot x and y values linear function

 

 

Graph of Linear Function y = 3x +3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

To be continued…

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