CBSE Class 8 Mathematics Introduction to Graphs Notes Set 08

Kinds of Graphs

A bar graph compares categories using bars of equal width. A pie chart compares parts of a whole. A histogram shows data grouped in class intervals with adjacent bars. A line graph shows how a quantity changes continuously over time by joining plotted points with line segments.

Coordinate Plane

Two perpendicular number lines meet at the origin O(0, 0). The horizontal one is the x-axis and the vertical one is the y-axis. They divide the plane into four quadrants.
A point (x, y) has abscissa x (distance along the x direction) and ordinate y. Signs: first quadrant (+, +), second (-, +), third (-, -), fourth (+, -).
Points on the x-axis have y = 0, for example (-5, 0); points on the y-axis have x = 0, for example (0, 7).

Distances

The distance of P(x, y) from the x-axis is |y| and from the y-axis is |x|. Distance is never negative.
The distance of P(x, y) from the origin is the square root of (x² + y²); for (3, 4) it is 5 units. Two points on the x-axis are |x2 - x1| apart; two points on the y-axis are |y2 - y1| apart.

Variables

A variable is a quantity that can take different values. If a change in one quantity causes a change in another, the first is the independent variable and the second the dependent variable. For example, as time increases the interest earned increases: time is independent and interest is dependent. The independent variable is placed on the horizontal axis.

Drawing a Line Graph

Choose a suitable scale for each axis, plot the points from the table, and join consecutive points. A jagged mark on an axis shows that the numbers between 0 and the first value are skipped. Values between two plotted points can be estimated by assuming a uniform change along the segment.