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Graphical Methods - Mathematics Form 3

GRAPHICAL METHODS

A graph is a pictorial representation of statistical data of a functional relationship between variables. Graphs show general tendencies in the quantitative behaviour of data and could serve a predictive function.

Examples:

i). Rainfall distribution during different months of the year.
ii). Children born in different days of the week, e.t.c.
iii). The length of different types of leaves.
iv). The number of Children in Different families.
v). Types of vehicles passing by a given point in different times.
vi). Population growth in different countries
vii). Number of trees planted during the short and long rains
.


to insert a picture of a graph

These are examples of questions on:

(i) Independent variable

If it is a rainfall distribution graph, what was the amount of rainfall in any given month?

(ii) Dendent variable

Which months had say 100mm of rainfall and above?


Drawing graphs of relations

In this topic we need to remind ourselves the procedures of drawing a graph.
To be able to draw suitable graphs of given relationships one must start by constructing the table of values for the relation. After obtaining the table for relations, the graphs are then drawn by:
i)Obtaining a suitable scale for the values in both the x and y axis.
ii)Plotting the content x and y variables.
iii)Joining the plotted variables to obtain a suitable graph.
Example 1

Draw the graph of the following equations

y =2 x - 5







Introduction

In analytical geometry graphs are used to represent functions of two variables on a Cartesian coordinate system, which is composed of horizontal x-axis or abscissa, and a vertical y-axis or ordinate. Each axis is a real number line and their intersection at zero point of each is called the origin. A graph in this sense is the locus of all points
(x, y) that satisfy a particular function. Most graphs employ two axes, in which the horizontal axis represents a group of dependent variables. On a plane the graphs take various forms, for example


1. y = ax + b is a linear graph


2. y = ax2
+ bx + c is a quadratic graph






Solution
Draw the tangent at x = 1.5, then take any two convinient points of the tangent for example (x1
,y1
) = (1, 1.8) and (x2
,y2
) = (2.5, -6).


Therefore, the gradient of the line =

Gradient = -5.2

The rate of change at x = 1.5 is -5. 2.


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