# PROPERTIES OF LINE GRAPHS

Line graphs consist of straight line segments or curves.

They are used to show how one quantity varies in relation to another

Since the quantities may take different values, we say they are variables.

In general when quantities vary, one is dependent on the other.

We say that the dependent variable depends on the independent variable.

Note :

The independent variable is placed on the horizontal axis and the dependent variable is placed on the vertical axis.

We join the dots together either with a smooth curve or with straight line segments.

The graph below is a line graph which connects the dots. Example 1 :

For each of the following graphs, state the dependent and independent variables: Solution :

Time is on x axis, so it is independent.

Distance is on y axis, so it is dependent.

Example 2 : Solution :

Time is on x axis, so it is independent.

Temperature is on y axis, so it is dependent.

Example 3 :

For each graph, state whether it is:

A) increasing

B) decreasing

C) increasing in some sections and decreasing in others Solution :

(a) By observing the given graph from left to right, it is increasing.

So option A is correct.

(b)  By observing the graph from left to right, it is increasing somewhere and decreasing somewhere.

So, increasing in some sections and decreasing in others option C is correct.

(c)  By observing the graph from left to right, it is decreasing.

So, option B is correct.

Example 4 :

This data set shows the speed of a runner at various times during a cross country race. a) State which is the dependent and which is the  independent variable.

b) Draw a point graph to display the data. Make sure the independent variable is on the horizontal axis.

c) Connect the points on your graph with straight line segments to form a line graph.

Solution :

(a)  Time should be placed on x-axis, speed should be placed on y-axis.

Time ==>  x-axis ==> independent

Speed ==>  y-axis ==> dependent

(b and c) Example 5 :

The data set below records the progress of a speed skater in a 500 m race.

 Time(s)0510152025303539.6 Distance(m)03479142226291350429500

a) State which is the dependent and which is the independent variable.

b) Draw a point graph to display the data. Make sure the independent variable is on the horizontal axis.

c) Connect the points on your graph with a smooth curve.

d) Comment on whether the graph is decreasing or increasing.

Solution :

(a)  On x axis, we place time. So, time is independent and distance is dependent.

(b) & (c) (d)  The graph is increasing. Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

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