Draw a linear graph for the following data: x: 2, 3, 6, 8 y: 12, 18, 36, 48

To draw a linear graph based on the given data points, we will treat the 'x' values as coordinates on the x-axis and the 'y' values as coordinates on the y-axis. This is a way to visually represent the relationship between two sets of numerical data.
Here are the steps to draw a linear graph:

Prepare Your Graph Paper or Graphing Tool:

Make sure you have graph paper or a digital graphing tool that has a clearly marked x-axis and y-axis.


Label the Axes:

The x-axis will represent the x-values (2, 3, 6, 8).
The y-axis will represent the y-values (12, 18, 36, 48).


Plot the Points:

Start by plotting the following points on the graph, where each pair is a ( x , y ) pair:
(2, 12)
(3, 18)
(6, 36)
(8, 48)




Draw the Line:

Because the relationship given is likely linear, try to draw a straight line that best fits or passes through these points. This line will likely connect them all or pass very closely through them due to the linear relationship.


Determine the Equation (Optional):

You can notice that for each increase in x, y increases by a proportional factor, suggesting a linear relationship of the form y = m x because the line passes through the origin. To find the constant of proportionality (slope), choose two points:
Calculate the slope m as x 2 ​ − x 1 ​ y 2 ​ − y 1 ​ ​ which can be from points (2, 12) and (8, 48) giving us m = 8 − 2 48 − 12 ​ = 6 .


Therefore the equation representing this linear relationship is y = 6 x .


Interpret the Graph if Needed:

This graph can be used to understand how changes in 'x' values affect 'y' values, representing a direct proportionality.



This concise method provides a simple way of understanding linear graphs and can be extended to other datasets as well.

Answered by LiamAlexanderSmith | 2025-07-21