NCERT Solutions Class 8 Maths Chapter 12 — Introduction to Graphs

Solution:

Step 1: Graphs are powerful tools because they provide a visual summary of data.

Step 2: This visual representation makes it significantly easier to identify patterns, compare different values, and understand relationships or trends that might be difficult to spot when data is presented only in tables or text.

Solution:

Step 1: By convention, the horizontal number line in a Cartesian coordinate system is designated as the x-axis.

Step 2: The vertical number line is designated as the y-axis.

Step 3: The point where the x-axis and y-axis intersect is called the origin, with coordinates (0,0).

Solution:

Step 1: The phrase '3 units to the right of the y-axis' corresponds to a positive x-coordinate, so x = 3.

Step 2: The phrase '5 units above the x-axis' corresponds to a positive y-coordinate, so y = 5.

Step 3: Therefore, the coordinates of point P are (x, y) = (3, 5).

Solution:

Step 1: Bar graphs represent discrete categories, meaning there are distinct gaps between categories, so their bars do not touch.

Step 2: Histograms represent continuous data grouped into class intervals. Since these intervals are continuous, the bars in a histogram touch each other to show the continuous nature of the data.

Step 3: Both bar graphs and histograms can use vertical bars (most common) and should always have titles.

Solution:

Step 1: List the number of students for each activity: Art (30), Music (25), Dance (40), Drama (15).

Step 2: Order them from highest to lowest: Dance (40), Art (30), Music (25), Drama (15).

Step 3: The second-highest number of students chose Art.