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What is a Graph?

  • A graph is like a picture that shows how one thing changes when another thing changes. In the picture, there is a line that can be straight or curved. 
  • The line helps us understand the connection between two things.
  • In the relationship between these two things, we have one thing that we can change on purpose. This thing is called the independent variable. 
  • The other thing changes because of this, and it is called the dependent variable. Usually, in the picture, the thing we change on purpose is shown on the horizontal line (left to right), and the other thing is shown on the vertical line (up and down). 
  • For example, if we want to show a picture of how voltage (the thing we change) affects current (the thing that changes), we put voltage on the left-right line and current on the up-down line.

Graphs for Physics | Physics for JEE Main & AdvancedExample of a Graph

Common Graph Forms

Linear Relationship 

Equation: �=��+�y = mx+b
Description: A straight line graph where m is the slope (steepness) of the line, and b is the y-intercept (where the line crosses the y-axis).
Graphs for Physics | Physics for JEE Main & Advanced

Quadratic Equation/ Parabola

Equation: y = ax+ bx + c

Description: Quadratic graphs are graphs of a quadratic function and can be recognized as they include a squared term.
The shape of a quadratic graph is a parabola. 
The graphs have one tuning point – a minimum point or a maximum point.  
Graphs for Physics | Physics for JEE Main & Advanced

Cubic Graph

Cubic graphs are graphs of a cubic function and can be recognized as they include a cubed term.
E.g. An �3x3 term.
The graphs often have two turning points – a minimum point and a maximum point.
Graphs for Physics | Physics for JEE Main & Advanced

Exponential graphs

Exponential graphs are graphs of an exponential function and can be recognized as they include a ��kx term where k is the base and x is the exponent (power). The graphs can be a growth curve when k is greater than 11 or a decay curve when k is less than 11.

Graphs for Physics | Physics for JEE Main & Advanced

Reciprocal graph/ Inverse Proportionality 

Reciprocal graphs are graphs of a reciprocal function and can be recognized as they include a 1�1/x term.
Graphs for Physics | Physics for JEE Main & Advanced

Circle Graph 

They are of the form:
x2 + y2 = r2
where r2 is the radius of the circle.

Graphs for Physics | Physics for JEE Main & Advanced

Example 1: Match the graph with its equation

Graphs for Physics | Physics for JEE Main & Advanced

Equation 1: y = 2x                 
Equation 2: y = x+ x - 2
Equation 3:  x+ y= 4
Equation 4: y = x3- x - 2
Sol: 
Graph A has 2 vertices; it is very likely to be a cubic function.
Equation 4 is a cubic function with a y-intercept at −2 which is at the end of the equation when x=0
Graph B is a growth curve so its equation will have a term with x as an exponent (power); equation 1 has a term with x as an exponent.
There is a parabola graph, so this is the graph of a quadratic function that has a �2x2 term. Graph C is Equation 22
There is a circle graph.  It has a center (0,0) and radius 2; so its equation would be:
x2+y2=22
Graph D is Equation 3

Graphs for Physics | Physics for JEE Main & Advanced

Example 2: Recognise the types of graphs:

Graphs for Physics | Physics for JEE Main & Advanced

Equation 1: x+y=5              
Equation 2: y=5/x
Equation 3:  x2+y2=25
Equation 4: y=0.5x
Sol:
There is a straight line graph so this is the graph of a linear function that has no visible powers. There is no parabola graph so there is no quadratic function.
Graph B is Equation 11
There is a circle graph.  It has a center (0,0) so its equation would be:

x2+y2=r2
Graph A is Equation 33
Graph C is not a growth curve but it is a decay curve so its equation will have a term with x as an exponent (power).  Equation 44 has a term with x as an exponent.
Graph D is a curve in which 1/x has 22 sections in different quadrants of the coordinate grid.  It is likely to be a reciprocal graph with a 1�term.  Equation 22 has a term with  x as a denominator of a fraction.

Graphs for Physics | Physics for JEE Main & Advanced

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FAQs on Graphs for Physics - Physics for JEE Main & Advanced

1. What is a graph and how is it related to physics?
Ans. In physics, a graph is a visual representation of data or information that helps to understand relationships and patterns. Graphs are commonly used to represent physical phenomena, such as motion, force, and energy. By plotting variables on the x and y axes, graphs allow us to analyze and interpret data in a more intuitive way.
2. What are the different types of graphs used in physics?
Ans. There are several types of graphs commonly used in physics, including line graphs, bar graphs, scatter plots, and histograms. Line graphs are used to show the relationship between two variables, while bar graphs are used to compare different categories or groups. Scatter plots display the correlation between two variables, and histograms represent the frequency distribution of a set of data.
3. How can graphs be used to analyze motion in physics?
Ans. Graphs are extensively used to analyze motion in physics. By plotting distance or position on the y-axis and time on the x-axis, a graph can show the motion of an object. The slope of the line on the graph represents the object's velocity, and the area under the line represents the object's displacement. Graphs can also be used to analyze acceleration by examining the curvature or steepness of the line.
4. How do graphs help in understanding scientific experiments in physics?
Ans. Graphs play a crucial role in understanding scientific experiments in physics. They allow researchers to visually analyze data and identify patterns or trends. By plotting independent and dependent variables on a graph, researchers can observe how changes in one variable affect another. This helps in drawing conclusions, making predictions, and understanding the underlying principles or laws governing the experiment.
5. What are the advantages of using graphs in physics?
Ans. The use of graphs in physics offers several advantages. Firstly, graphs provide a visual representation of data, making it easier to interpret complex information. They allow for easy identification of trends, patterns, and relationships between variables. Additionally, graphs enable researchers to analyze and compare data more effectively, facilitating the identification of anomalies or outliers. Overall, graphs enhance the understanding and communication of scientific concepts in physics.
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