Introduction to Graphs

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# Introduction to Graphs - PowerPoint PPT Presentation

##### Introduction to Graphs

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1. Introduction to Graphs

2. INTRODUCTION • Line graphs illustrate the relationships between two variables, showing graphically what happens to one variable when the other changes. • Representation of equations by means of graphs • They give a visual picture of the behaviour of the two variables • Graphical approaches to problem solving are often easier to carry out than mathematical ones • They are less accurate, since the answers must be read from the graph and hence cannot be more accurate than the thickness of the pencil

3. BASIC PRINCIPLES OF GRAPHS • A graph is a diagram illustrating one or more mathematical relationships between two variables. • The y-axis is the vertical axis and usually displays the dependent variable – i.e. the variable which changes according to changes in the other variable • he x-axis is the horizontal axis and usually displays the independent variable – i.e. the variable which causes change in the other variable. • Scale used must be clear to the reader. • The scale need not be the same on both axes. • Each axis should be titled to show clearly both what it represents and the units of measurement.

4. The area within the axes (known as the plot area) is divided into a grid by reference to the scale on the axes. • Particular points within the graph are identified by a pair of numbers called co-ordinates which fix a point by reference to the scales along the axes. The first co-ordinate number always refers to a value on the scale along the x-axis and the second to the scale on the y- axis • The point at which the two axes meet is called the origin. This has the co-ordinate reference (0,0). • Finally, note that the x and y-axes may extend to include negative numbers

5. Drawing a Graph • Determine the range of values which will need to be shown on each of the axes. • Draw the axes and mark off the scales along them. • The aim is usually to draw as large a graph as possible since this will make it easier to plot the co-ordinates accurately, and also make it easier to read • The scales must be consistent along each axis, but do not need to be the same on both • Give each axis a title, number the main divisions along each scale and give the whole graph a title.

6. GRAPHING THE FUNCTIONS OF A VARIABLE

7. Representation • The values in the table can be expressed as a pair of co-ordinates which may be plotted on a graph. The first figure is the value of x along the scale of the x (horizontal) axis, and the second figure is the value of y along the scale of the y (vertical) axis • Ordered Pairs : Another way of describing the varying values of x and y is by means of a set of ordered pairs. This is a very useful and helpful way of noting the points we required in the graphical representation of a function

8. GRAPHS OF EQUATIONS

9. Linear Equations

10. Characteristics of Straight-Line Graphs • Lines parallel to an axis • Lines through the origin • Parallel lines • Direction of slope • Intercepts

12. Equations with x as the Denominator

13. Exponential and Logarithmic Equations

15. Gradient of a Straight Line • We can easily calculate the gradient of a straight line joining two points from the co-ordinates of those points.